Sep. 1990 - Aug. 1992: Postdoctoral Research Fellow, Nordita, Copenhagen Aug. 1992 - Nov. 1992: Visiting Fellowship, University of Cambridge Dec. 1992 - Nov. 1994: Postdoctoral Research Fellow, High Altitude Observatory/NCAR, Boulder Dec. 1994 - Jan. 1996: Nordic Assistant Professor, Nordita, Copenhagen Feb. 1996 - Dec. 2000: Professor of Applied Mathematics, University of Newcastle upon Tyne Jan. 2000 - Dec. 2006: Professor of Astrophysics, Nordita (Copenhagen) since January 2007: Professor of Astrophysics, Nordita (Stockholm) and Stockholm Observatory
Abstract: The mechanisms for explaining how a stable asymmetric chemical system can be formed from a symmetric chemical system, in the absence of any asymmetric influence other than statistical fluctuations, have been developed during the last decades, focusing on the non-linear kinetic aspects. Besides the absolute necessity of self-amplification processes, the importance of energetic aspects is often underestimated. Going down to the most fundamental aspects, the distinction between a single object-that can be intrinsically asymmetric-and a collection of objects-whose racemic state is the more stable one-must be emphasized. A system of strongly interacting objects can be described as one single object retaining its individuality and a single asymmetry; weakly or non-interacting objects keep their own individuality, and are prone to racemize towards the equilibrium state. In the presence of energy fluxes, systems can be maintained in an asymmetric non-equilibrium steady-state. Such dynamical systems can retain their asymmetry for times longer than their racemization time.
Abstract: In this study we provide the first numerical demonstration of the effects of turbulence on the mean Lorentz force and the resulting formation of large-scale magnetic structures. Using three-dimensional direct numerical simulations (DNS) of forced turbulence we show that an imposed mean magnetic field leads to a decrease of the turbulent hydromagnetic pressure and tension. This phenomenon is quantified by determining the relevant functions that relate the sum of the turbulent Reynolds and Maxwell stresses with the Maxwell stress of the mean magnetic field. Using such a parameterization, we show by means of two-dimensional and three-dimensional mean-field numerical modelling that an isentropic density stratified layer becomes unstable in the presence of a uniform imposed magnetic field. This large-scale instability results in the formation of loop-like magnetic structures which are concentrated at the top of the stratified layer. In three dimensions these structures resemble the appearance of bipolar magnetic regions in the Sun. The results of DNS and mean-field numerical modelling are in good agreement with theoretical predictions. We discuss our model in the context of a distributed solar dynamo where active regions and sunspots might be rather shallow phenomena. (C) 2010 WILEYNCH Verlag GmbH &Co. KGaA. Weinheim
Abstract: Self-consistent convective dynamo simulations in wedge-shaped spherical shells are presented. Differential rotation is generated by the interaction of convection with rotation. Equatorward acceleration and dynamo action are obtained only for sufficiently rapid rotation. The angular velocity tends to be constant along cylinders. Oscillatory large-scale fields are found to migrate in the poleward direction. Comparison with earlier simulations in full spherical shells and Cartesian domains is made. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA. Weinheim
Abstract: We use direct numerical simulations of forced MHD turbulence with a forcing function that produces two different signs of kinetic helicity in the upper and lower parts of the domain. We show that the mean flux of magnetic helicity from the small-scale field between the two parts of the domain can be described by a Fickian diffusion law with a diffusion coefficient that is approximately independent of the magnetic Reynolds number and about one third of the estimated turbulent magnetic diffusivity. The data suggest that the turbulent diffusive magnetic helicity flux can only be expected to alleviate catastrophic quenching at Reynolds numbers of more than several thousands. We further calculate the magnetic helicity density and its flux in the domain for three different gauges. We consider the Weyl gauge, in which the electrostatic potential vanishes, the pseudo-Lorenz gauge, where the speed of light is replaced by the sound speed, and the 'resistive gauge' in which the Laplacian of the magnetic vector potential acts as a resistive term. We find that, in the statistically steady state, the time-averaged magnetic helicity density and the magnetic helicity flux are the same in all three gauges. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA. Weinheim
Abstract: Using three-dimensional convection simulations, it is shown that a sinusoidal variation of horizontal shear leads to a kinematic alpha effect with a similar sinusoidal variation. The effect exists even for weak stratification and arises owing to the inhomogeneity of turbulence and the presence of impenetrable vertical boundaries. This system produces large-scale magnetic fields that also show a sinusoidal variation in the cross-stream direction. It is argued that earlier investigations overlooked these phenomena partly because of the use of horizontal averaging and also because measurements of alpha using an imposed field combined with long time averages give erroneous results. It is demonstrated that in such cases the actual horizontally averaged mean field becomes non-uniform. The turbulent magnetic diffusion term resulting from such non-uniform fields can then no longer be neglected and begins to balance the alpha effect.
Abstract: The resistive decay of chains of three interlocked magnetic flux rings is considered. Depending on the relative orientation of the magnetic field in the three rings, the late-time decay can be either fast or slow. Thus, the qualitative degree of tangledness is less important than the actual value of the linking number or, equivalently, the net magnetic helicity. Our results do not suggest that invariants of higher order than that of the magnetic helicity need to be considered to characterize the decay of the field.
Abstract: We present direct numerical simulations of the equations of compressible magnetohydrodynamics in a wedge-shaped spherical shell, without shear, but with random helical forcing which has negative (positive) helicity in the northern (southern) hemisphere. We find a large-scalemagnetic field that is nearly uniform in the azimuthal direction and approximately antisymmetric about the equator. Furthermore, the large-scale field in each hemisphere oscillates on nearly dynamical timescales with reversals of polarity and equatorward migration. Corresponding mean-field models also show similar migratory oscillations with a frequency that is nearly independent of the magnetic Reynolds number. This mechanism may be relevant for understanding equatorward migration seen in the solar dynamo.
Abstract: Angular momentum transport due to hydrodynamic turbulent convection is studied using local three-dimensional numerical simulations employing the shearing box approximation. We determine the turbulent viscosity from non-rotating runs over a range of values of the shear parameter and use a simple analytical model in order to extract the non-diffusive contribution (Lambda-effect) to the stress in runs where rotation is included. Our results suggest that the turbulent viscosity is on the order of the mixing length estimate and weakly affected by rotation. The Lambda-effect is non-zero and a factor of 2-4 smaller than the turbulent viscosity in the slow rotation regime. We demonstrate that for Keplerian shear, the angular momentum transport can change sign and be outward when the rotation period is greater than the turnover time, i.e., when the Coriolis number is below unity. This result seems to be relatively independent of the value of the Rayleigh number.
Abstract: The turbulent diffusivity tensor is determined for linear shear-flow turbulence using numerical simulations. For moderately strong shear, the diagonal components are found to increase quadratically with Peclet and Reynolds numbers below about 10 and then become constant. The diffusivity tensor is found to have components proportional to the symmetric and antisymmetric parts of the velocity gradient matrix, as well as products of these. All components decrease with the wave number of the mean field in a Lorentzian fashion. The components of the diffusivity tensor are found not to depend significantly on the presence of helicity in the turbulence. The signs of the leading terms in the expression for the diffusion tensor are found to be in good agreement with estimates based on a simple closure assumption.
Abstract: We perform direct numerical simulations of forced and freely decaying 3D magnetohydrodynamic turbulence in order to model magnetic field evolution during cosmological phase transitions in the early Universe. Our approach assumes the existence of a magnetic field generated either by a process during inflation or shortly thereafter, or by bubble collisions during a phase transition. We show that the final configuration of the magnetic field depends on the initial conditions, while the velocity field is nearly independent of initial conditions.
Abstract: Using two- and three-dimensional hydromagnetic simulations for a range of different flows, including laminar and turbulent ones, it is shown that solutions expressing the field in terms of Euler potentials (EP) are in general incorrect if the EP are evolved with an artificial diffusion term. In three dimensions, standard methods using the magnetic vector potential are found to permit dynamo action when the EP give decaying solutions. With an imposed field, the EP method yields excessive power at small scales. This effect is more exaggerated in the dynamic case, suggesting an unrealistically reduced feedback from the Lorentz force. The EP approach agrees with standard methods only at early times when magnetic diffusivity did not have time to act. It is demonstrated that the usage of EP with even a small artificial magnetic diffusivity does not converge to a proper solution of hydromagnetic turbulence. The source of this disagreement is not connected with magnetic helicity or the three-dimensionality of the magnetic field, but is simply due to the fact that the non-linear representation of the magnetic field in terms of EP that depend on the same coordinates is incompatible with the linear diffusion operator in the induction equation.
Abstract: In mean-field magnetohydrodynamics the mean electromotive force due to velocity and magnetic-field fluctuations plays a crucial role. In general it consists of two parts, one independent of and another one proportional to the mean magnetic field. The first part may be nonzero only in the presence of mhd turbulence, maintained, e.g., by small-scale dynamo action. It corresponds to a battery, which lets a mean magnetic field grow from zero to a finite value. The second part, which covers, e.g., the a effect, is important for large-scale dynamos. Only a few examples of the aforementioned first art of the mean electromotive force have been discussed so far. It is shown that a mean electromotive force proportional to the mean fluid velocity, but independent of the mean magnetic field, may occur in an originally homogeneous isotropic mhd turbulence if there are nonzero correlations of velocity and electric current fluctuations or, what is equivalent, of vorticity and magnetic field fluctuations. This goes beyond the Yoshizawa effect, which consists in the Occurrence of mean electromotive forces proportional to the mean vorticity or to the angular velocity defining, the Coriolis force in a rotating frame and depends on the cross-helicity defined by the velocity and magnetic field fluctuations. Contributions to the mean electromotive force due to inhomogeneity of the turbulence are also considered. Possible consequences of the above findings for the generation of magnetic fields in cosmic bodies are discussed. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA. Weinheim
Abstract: WC Present local numerical models of accretion disk turbulence driven by the magnetorotational instability with varying shear rate. The resulting turbulent stresses are compared with predictions of a closure model in which triple correlations are modelled in terms of quadratic correlations. This local model uses live nondimensional parameters to describe the properties of the flow. We attempt to determine these Closure parameters for our simulations and find that the model does produce qualitatively correct behaviour. In addition, we present results concerning the shear rate dependency of the magnetic to kinetic energy ratio. We find both the turbulent stress ratio and the total stress to be strongly dependent on the shear rate. (C) 2009 WILEY-VCH Verlag GmbH & Co, KGaA, Weinheim
Abstract: WC Present local numerical models of accretion disk turbulence driven by the magnetorotational instability with varying shear rate. The resulting turbulent stresses are compared with predictions of a closure model in which triple correlations are modelled in terms of quadratic correlations. This local model uses live nondimensional parameters to describe the properties of the flow. We attempt to determine these Closure parameters for our simulations and find that the model does produce qualitatively correct behaviour. In addition, we present results concerning the shear rate dependency of the magnetic to kinetic energy ratio. We find both the turbulent stress ratio and the total stress to be strongly dependent on the shear rate. (C) 2009 WILEY-VCH Verlag GmbH & Co, KGaA, Weinheim
Abstract: Dynamo action owing to helically forced turbulence and large-scale shear is studied using direct numerical simulations. The resulting magnetic field displays propagating wave-like behavior. This behavior can be modeled in terms of an alpha Omega dynamo. In most cases super-equipartition fields are generated. By varying the fraction of helicity of the turbulence the regeneration of poloidal fields via the helicity effect (corresponding to the alpha-effect) is regulated. The saturation level of the magnetic field in the numerical models is consistent with a linear dependence on the ratio of the fractional helicities of the small and large-scale fields, as predicted by a simple nonlinear mean-field model. As the magnetic Reynolds number (Re-M) based on the wavenumber of the energy-carrying eddies is increased from 1 to 180, the cycle frequency of the large-scale field is found to decrease by a factor of about 6 in cases where the turbulence is fully helical. This is interpreted in terms of the turbulent magnetic diffusivity, which is found to be only weakly dependent on the Re M
Abstract: In the framework of mean-field electrodynamics the coefficients defining the mean electromotive force in Galloway-Proctor flows are determined. These flows show a two-dimensional pattern and are helical. The pattern wobbles in its plane. Apart from one exception a circularly polarized Galloway-Proctor flow, i.e. a circular motion of the flow pattern is assumed. This corresponds to one of the cases considered recently by Courvoisier, Hughes & Tobias. An analytic theory of the alpha effect and related effects in this flow is developed within the second-order correlation approximation and a corresponding fourth-order approximation. In the validity range of these approximations there is an alpha effect but no gamma effect, or pumping effect. Numerical results obtained with the test-field method, which are independent of these approximations, confirm the results for alpha and show that gamma is in general non-zero. Both alpha and gamma show a complex dependency on the magnetic Reynolds number and other parameters that define the flow, that is, amplitude and frequency of the circular motion. Some results for the magnetic diffusivity eta(t) and a related quantity are given, too. Finally, a result for a in the case of alpha randomly varying linearly polarized Galloway-Proctor flow, without the aforementioned circular motion, is presented. The flows investigated show quite interesting effects. There is, however, no straightforward way to relate these flows to turbulence and to use them for studying properties of the alpha effect and associated effects under realistic conditions.
Abstract: Simulations of stochastically forced shear-flow turbulence in a shearing-periodic domain are used to study the spontaneous generation of large-scale flow patterns in the direction perpendicular to the plane of the shear. Based on an analysis of the resulting large-scale velocity correlations it is argued that the mechanism behind this phenomenon could be the mean-vorticity dynamo effect pioneered by Elperin, Kleeorin, and Rogachevskii [Phys. Rev. E 68, 016311 (2003)]. This effect is based on the anisotropy of the eddy viscosity tensor. One of its components may be able to replenish cross-stream mean flows by acting upon the streamwise component of the mean flow. Shear, in turn, closes the loop by acting upon the cross-stream mean flow to produce stronger streamwise mean flows. The diagonal component of the eddy viscosity is found to be of the order of the rms turbulent velocity divided by the wave number of the energy-carrying eddies.
Abstract: We use three-dimensional direct numerical simulations of the helically forced magnetohydrodynamic equations in spherical shell segments in order to study the effects of changes in the geometrical shape and size of the domain on the growth and saturation of large-scale magnetic fields. We inject kinetic energy along with kinetic helicity in spherical domains via helical forcing using Chandrasekhar-Kendall functions. We take perfect conductor boundary conditions for the magnetic field to ensure that no magnetic helicity escapes the domain boundaries. We find dynamo action giving rise to magnetic fields at scales larger than the characteristic scale of the forcing. The magnetic energy exceeds the kinetic energy over dissipative timescales, similar to that seen earlier in Cartesian simulations in periodic boxes. As we increase the size of the domain in the azimuthal direction, we find that the nonlinearly saturated magnetic field organizes itself in long-lived cellular structures with aspect ratios close to unity. These structures tile the domain along the azimuthal direction, thus resulting in very small longitudinally averaged magnetic fields for large domain sizes. The scales of these structures are determined by the smallest scales of the domain, which in our simulations is usually the radial scale. We also find that increasing the meridional extent of the domains produces little qualitative change, except a marginal increase in the large-scale field. We obtain qualitatively similar results in Cartesian domains with similar aspect ratios.
Abstract: Recent analytical and computational advances in the theory of large-scale dynamos are reviewed. The importance of the magnetic helicity constraint is apparent even without invoking mean-field theory. The tau approximation yields expressions that show how the magnetic helicity gets incorporated into mean-field theory. The test-field method allows an accurate numerical determination of turbulent transport coefficients in linear and nonlinear regimes. Finally, some critical views on the solar dynamo are being offered and targets for future research are highlighted.
Abstract: Aims. We study the dependence of turbulent transport coefficients, such as the components of the alpha tensor (alpha(ij)) and the turbulent magnetic diffusivity tensor (eta(ij)), on shear and magnetic Reynolds number in the presence of helical forcing. Methods. We use three-dimensional direct numerical simulations with periodic boundary conditions and measure the turbulent transport coefficients using the kinematic test field method. In all cases the magnetic Prandtl number is taken as unity. Results. We find that with increasing shear the diagonal components of alpha(ij) quench, whereas those of eta(ij) increase. The antisymmetric parts of both tensors increase with increasing shear. We also propose a simple expression for the turbulent pumping velocity (or gamma effect). This pumping velocity is proportional to the kinetic helicity of the turbulence and the vorticity of the mean flow. For negative helicity, i.e. for a positive trace of alpha(ij), it points in the direction of the mean vorticity, i.e. perpendicular to the plane of the shear flow. Our simulations support this expression for low shear and magnetic Reynolds number. The transport coefficients depend on the wavenumber of the mean flow in a Lorentzian fashion, just as for non-shearing turbulence.
Abstract: Aims. We study turbulent transport coefficients that describe the evolution of large-scale magnetic fields in turbulent convection. Methods. We use the test field method, together with three-dimensional numerical simulations of turbulent convection with shear and rotation, to compute turbulent transport coefficients describing the evolution of large-scale magnetic fields in mean-field theory in the kinematic regime. We employ one-dimensional mean-field models with the derived turbulent transport coefficients to examine whether they give results that are compatible with direct simulations. Results. The results for the alpha-effect as a function of rotation rate are consistent with earlier numerical studies, i.e. increasing magnitude as rotation increases and approximately cos theta latitude profile for moderate rotation. Turbulent diffusivity, eta(t), is proportional to the square of the turbulent vertical velocity in all cases. Whereas eta(t) decreases approximately inversely proportional to the wavenumber of the field, the alpha-effect and turbulent pumping show a more complex behaviour with partial or full sign changes and the magnitude staying roughly constant. In the presence of shear and no rotation, a weak alpha-effect is induced which does not seem to show any consistent trend as a function of shear rate. Provided that the shear is large enough, this small alpha-effect is able to excite a dynamo in the mean-field model. The coefficient responsible for driving the shear-current effect shows several sign changes as a function of depth but is also able to contribute to dynamo action in the mean-field model. The growth rates in these cases are, however, well below those in direct simulations, suggesting that an incoherent alpha-shear dynamo may also act in the simulations. If both rotation and shear are present, the alpha-effect is more pronounced. At the same time, the combination of the shear-current and Omega x J-effects is also stronger than in the case of shear alone, but subdominant to the alpha-shear dynamo. The results of direct simulations are consistent with mean-field models where all of these effects are taken into account without the need to invoke incoherent effects.
Abstract: Selected topics in solar dynamo theory are being highlighted. The possible relevance of the near-surface shear lawyer is discussed. The role of turbulent; downward pumping is mentioned in connection with earlier concerns that a dynamo-generated magnetic field would be rapidly lost, from the convection zone by magnetic buoyancy. It is argued that shear-mediated small-scale magnetic helicity fluxes are responsible for the success of some of the recent largescale dynamo simulations. These fluxes help in disposing of excess small-scale magnetic helicity. This small-scale magnetic helicity, in turn, is generated in response to the production of an overall tilt in each Parker loop. Some preliminary calculations of this helicity flux are presented for a system with uniform shear. In the Sun the effects of magnetic helicity fluxes may be seen in coronal mass ejections shedding large amounts of magnetic helicity.
Abstract: The turbulent diffusion tensor describing the evolution of the mean concentration of a passive scalar is investigated for non-helically forced turbulence in the presence of rotation or a magnetic field. With rotation, the Coriolis force causes a sideways deflection of the flux of mean concentration. Within the magnetohydrodynamics approximation there is no analogous effect from the magnetic field because the effects on the flow do not depend on the sign of the field. Both rotation and magnetic fields tend to suppress turbulent transport, but this suppression is weaker in the direction along the magnetic field. Turbulent transport along the rotation axis is not strongly affected by rotation, except on shorter length-scales, i.e. when the scale of the variation of the mean field becomes comparable with the scale of the energy-carrying eddies. These results are discussed in the context of anisotropic convective energy transport in the Sun.
Abstract: Aims. We study the dependence of turbulent transport coefficients, such as the components of the alpha tensor (alpha(ij)) and the turbulent magnetic diffusivity tensor (eta(ij)), on shear and magnetic Reynolds number in the presence of helical forcing. Methods. We use three-dimensional direct numerical simulations with periodic boundary conditions and measure the turbulent transport coefficients using the kinematic test field method. In all cases the magnetic Prandtl number is taken as unity. Results. We find that with increasing shear the diagonal components of alpha(ij) quench, whereas those of eta(ij) increase. The antisymmetric parts of both tensors increase with increasing shear. We also propose a simple expression for the turbulent pumping velocity (or gamma effect). This pumping velocity is proportional to the kinetic helicity of the turbulence and the vorticity of the mean flow. For negative helicity, i.e. for a positive trace of alpha(ij), it points in the direction of the mean vorticity, i.e. perpendicular to the plane of the shear flow. Our simulations support this expression for low shear and magnetic Reynolds number. The transport coefficients depend on the wavenumber of the mean flow in a Lorentzian fashion, just as for non-shearing turbulence.
Abstract: Simulations of stochastically forced shear-flow turbulence in a shearing-periodic domain are used to study the spontaneous generation of large-scale flow patterns in the direction perpendicular to the plane of the shear. Based on an analysis of the resulting large-scale velocity correlations it is argued that the mechanism behind this phenomenon could be the mean-vorticity dynamo effect pioneered by Elperin, Kleeorin, and Rogachevskii [Phys. Rev. E 68, 016311 (2003)]. This effect is based on the anisotropy of the eddy viscosity tensor. One of its components may be able to replenish cross-stream mean flows by acting upon the streamwise component of the mean flow. Shear, in turn, closes the loop by acting upon the cross-stream mean flow to produce stronger streamwise mean flows. The diagonal component of the eddy viscosity is found to be of the order of the rms turbulent velocity divided by the wave number of the energy-carrying eddies.
Abstract: Recent analytical and computational advances in the theory of large-scale dynamos are reviewed. The importance of the magnetic helicity constraint is apparent even without invoking mean-field theory. The tau approximation yields expressions that show how the magnetic helicity gets incorporated into mean-field theory. The test-field method allows an accurate numerical determination of turbulent transport coefficients in linear and nonlinear regimes. Finally, some critical views on the solar dynamo are being offered and targets for future research are highlighted.
Abstract: We use three-dimensional direct numerical simulations of the helically forced magnetohydrodynamic equations in spherical shell segments in order to study the effects of changes in the geometrical shape and size of the domain on the growth and saturation of large-scale magnetic fields. We inject kinetic energy along with kinetic helicity in spherical domains via helical forcing using Chandrasekhar-Kendall functions. We take perfect conductor boundary conditions for the magnetic field to ensure that no magnetic helicity escapes the domain boundaries. We find dynamo action giving rise to magnetic fields at scales larger than the characteristic scale of the forcing. The magnetic energy exceeds the kinetic energy over dissipative timescales, similar to that seen earlier in Cartesian simulations in periodic boxes. As we increase the size of the domain in the azimuthal direction, we find that the nonlinearly saturated magnetic field organizes itself in long-lived cellular structures with aspect ratios close to unity. These structures tile the domain along the azimuthal direction, thus resulting in very small longitudinally averaged magnetic fields for large domain sizes. The scales of these structures are determined by the smallest scales of the domain, which in our simulations is usually the radial scale. We also find that increasing the meridional extent of the domains produces little qualitative change, except a marginal increase in the large-scale field. We obtain qualitatively similar results in Cartesian domains with similar aspect ratios.
Abstract: The existence of large-scale dynamos in rigidly rotating turbulent convection without shear is studied using three-dimensional numerical simulations of penetrative rotating compressible convection. We demonstrate that rotating convection in a Cartesian domain can drive a large-scale dynamo even in the absence of shear. The large-scale field contains a significant fraction of the total field in the saturated state. The simulation results are compared with one-dimensional mean-field dynamo models where turbulent transport coefficients, as determined using the test field method, are used. The reason for the absence of large-scale dynamo action in earlier studies is shown to be due to the rotation being too slow: whereas the alpha-effect can change sign, its magnitude stays approximately constant as a function of rotation, and the turbulent diffusivity decreases monotonically with increasing rotation. Only when rotation is rapid enough a large-scale dynamo can be excited. The one-dimensional mean-field model with dynamo coefficients from the test-field results predicts reasonably well the dynamo excitation in the direct simulations. This result further validates the test field procedure and reinforces the interpretation that the observed dynamo is driven by a turbulent alpha-effect. This result demonstrates the existence of an alpha-effect and an alpha(2)-dynamo with natural forcing.
Abstract: Using direct simulations of hydromagnetic turbulence driven by random polarized waves it is shown that dynamo action is possible over a wide range of magnetic Prandtl numbers from 10(-3) to 1. Triply periodic boundary conditions are being used. In the final saturated state the resulting magnetic field has a large-scale component of Beltrami type. For the kinematic phase, growth rates have been determined for magnetic Prandtl numbers between 0.01 and 1, but only the case with the smallest magnetic Prandtl number shows large-scale magnetic fields. It is less organized than in the nonlinear stage. For small magnetic Prandtl numbers the growth rates are comparable to those calculated from an alpha squared mean-field dynamo. In the linear regime the magnetic helicity spectrum has a short inertial range compatible with a -5/3 power law, while in the nonlinear regime it is the current helicity whose spectrum may be compatible with such a law. In the saturated case, the spectral magnetic energy in the inertial range is in slight excess over the spectral kinetic energy, although for small magnetic Prandtl numbers the magnetic energy spectrum reaches its resistive cut off wavenumber more quickly. The viscous energy dissipation declines with the square root of the magnetic Prandtl number, which implies that most of the energy is dissipated via Joule heat.
Abstract: The turbulent diffusion tensor describing the evolution of the mean concentration of a passive scalar is investigated for non-helically forced turbulence in the presence of rotation or a magnetic field. With rotation, the Coriolis force causes a sideways deflection of the flux of mean concentration. Within the magnetohydrodynamics approximation there is no analogous effect from the magnetic field because the effects on the flow do not depend on the sign of the field. Both rotation and magnetic fields tend to suppress turbulent transport, but this suppression is weaker in the direction along the magnetic field. Turbulent transport along the rotation axis is not strongly affected by rotation, except on shorter length-scales, i.e. when the scale of the variation of the mean field becomes comparable with the scale of the energy-carrying eddies. These results are discussed in the context of anisotropic convective energy transport in the Sun.
Abstract: In the framework of mean-field electrodynamics the coefficients defining the mean electromotive force in Galloway-Proctor flows are determined. These flows show a two-dimensional pattern and are helical. The pattern wobbles in its plane. Apart from one exception a circularly polarized Galloway-Proctor flow, i.e. a circular motion of the flow pattern is assumed. This corresponds to one of the cases considered recently by Courvoisier, Hughes & Tobias. An analytic theory of the alpha effect and related effects in this flow is developed within the second-order correlation approximation and a corresponding fourth-order approximation. In the validity range of these approximations there is an alpha effect but no gamma effect, or pumping effect. Numerical results obtained with the test-field method, which are independent of these approximations, confirm the results for alpha and show that gamma is in general non-zero. Both alpha and gamma show a complex dependency on the magnetic Reynolds number and other parameters that define the flow, that is, amplitude and frequency of the circular motion. Some results for the magnetic diffusivity eta(t) and a related quantity are given, too. Finally, a result for a in the case of alpha randomly varying linearly polarized Galloway-Proctor flow, without the aforementioned circular motion, is presented. The flows investigated show quite interesting effects. There is, however, no straightforward way to relate these flows to turbulence and to use them for studying properties of the alpha effect and associated effects under realistic conditions.
Abstract: Selected topics in solar dynamo theory are being highlighted. The possible relevance of the near-surface shear lawyer is discussed. The role of turbulent; downward pumping is mentioned in connection with earlier concerns that a dynamo-generated magnetic field would be rapidly lost, from the convection zone by magnetic buoyancy. It is argued that shear-mediated small-scale magnetic helicity fluxes are responsible for the success of some of the recent largescale dynamo simulations. These fluxes help in disposing of excess small-scale magnetic helicity. This small-scale magnetic helicity, in turn, is generated in response to the production of an overall tilt in each Parker loop. Some preliminary calculations of this helicity flux are presented for a system with uniform shear. In the Sun the effects of magnetic helicity fluxes may be seen in coronal mass ejections shedding large amounts of magnetic helicity.
Abstract: Using direct simulations of hydromagnetic turbulence driven by random polarized waves it is shown that dynamo action is possible over a wide range of magnetic Prandtl numbers from 10(-3) to 1. Triply periodic boundary conditions are being used. In the final saturated state the resulting magnetic field has a large-scale component of Beltrami type. For the kinematic phase, growth rates have been determined for magnetic Prandtl numbers between 0.01 and 1, but only the case with the smallest magnetic Prandtl number shows large-scale magnetic fields. It is less organized than in the nonlinear stage. For small magnetic Prandtl numbers the growth rates are comparable to those calculated from an alpha squared mean-field dynamo. In the linear regime the magnetic helicity spectrum has a short inertial range compatible with a -5/3 power law, while in the nonlinear regime it is the current helicity whose spectrum may be compatible with such a law. In the saturated case, the spectral magnetic energy in the inertial range is in slight excess over the spectral kinetic energy, although for small magnetic Prandtl numbers the magnetic energy spectrum reaches its resistive cut off wavenumber more quickly. The viscous energy dissipation declines with the square root of the magnetic Prandtl number, which implies that most of the energy is dissipated via Joule heat.
Abstract: Estimates for the non-linear alpha effect in helical turbulence with an applied magnetic field are presented using two different approaches: the imposed-field method where the electromotive force owing to the applied field is used, and the test-field method where separate evolution equations are solved for a set of different test fields. Both approaches agree for stronger fields, but there are apparent discrepancies for weaker fields that can be explained by the influence of dynamo-generated magnetic fields on the scale of the domain that are referred to as meso-scale magnetic fields. Examples are discussed where these meso-scale fields can lead to both drastically overestimated and underestimated values of alpha compared with the kinematic case. It is demonstrated that the kinematic value can be recovered by resetting the fluctuating magnetic field to zero in regular time intervals. It is concluded that this is the preferred technique both for the imposed-field and the test-field methods.
Abstract: Using mean-field models with a dynamical quenching formalism, we show that in finite domains magnetic helicity fluxes associated with small-scale magnetic fields are able to alleviate catastrophic quenching. We consider fluxes that result from advection by a mean flow, the turbulent mixing down the gradient of mean small-scale magnetic helicity density or the explicit removal which may be associated with the effects of coronal mass ejections in the Sun. In the absence of shear, all the small-scale magnetic helicity fluxes are found to be equally strong for both large-and small-scale fields. In the presence of shear, there is also an additional magnetic helicity flux associated with the mean field, but this flux does not alleviate catastrophic quenching. Outside the dynamo-active region, there are neither sources nor sinks of magnetic helicity, so in a steady state this flux must be constant. It is shown that unphysical behaviour emerges if the small-scale magnetic helicity flux is forced to vanish within the computational domain.
Abstract: The effects of uniform horizontal shear on a stably stratified layer of gas is studied. The system is initially destabilized by a magnetically buoyant flux tube pointing in the cross-stream direction. The shear amplifies the initial field to Lundquist numbers of about 200-400, but then its value drops to about 100-300, depending on the value of the sub-adiabatic gradient. The larger values correspond to cases where the stratification is strongly stable and nearly isothermal. At the end of the runs the magnetic field is nearly axisymmetric, i.e. uniform in the streamwise direction. In view of Cowling's theorem the sustainment of the field remains a puzzle and may be due to subtle numerical effects that have not yet been identified in detail. In the final state the strength of the magnetic field decreases with height in such a way that the field is expected to be unstable. Low amplitude oscillations are seen in the vertical velocity even at late times, suggesting that they might be persistent. (C) 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Abstract: The generation of mean magnetic fields is Studied for a simple non-helical flow where a net cross-helicity of either sign call emerge. This flow, which is also known as the Archontis flow, is a generalization of the Arnold-Beltrami-Childress flow, but with the cosine terms omitted. The presence of cross-helicity leads to a mean-field dynamo effect that is known as the Yoshizawa effect. Direct numerical simulations of Such flows demonstrate the presence of magnetic fields oil scales larger than the scale of: the flow. Contrary to earlier expectations, the Yoshizawa effect is found to be proportional to the mean magnetic field and can therefore lead to its exponential instead Of just linear amplification for magnetic Reynolds numbers that exceed a certain critical Value. Unlike alpha effect dynamos, it is found that the Yoshizawa effect is not notably constrained by the presence of a conservation law. It is argued that this is due to the presence of a forcing term in the momentum equation, which leads to a non-zero correlation with the magnetic field. Finally, the application to energy convergence in solar wind turbulence is discussed.
Abstract: The role of magnetic helicity in astrophysical large-scale dynamos is reviewed and compared with cases where there is no energy supply and an initial magnetic field can only decay. In both cases magnetic energy tends to get redistributed to larger scales. Depending on the efficiency of magnetic helicity fluxes the decay of a helical field can speed up. Likewise, the saturation of a helical dynamo can speed up through magnetic helicity fluxes. The astrophysical importance of these processes is reviewed in the context of the solar dynamo and an estimated upper limit for the magnetic helicity flux of 10(46) Mx(2)/cycle is given.
Abstract: The mechanisms for explaining how a stable asymmetric chemical system can be formed from a symmetric chemical system, in the absence of any asymmetric influence other than statistical fluctuations, have been developed during the last decades, focusing on the non-linear kinetic aspects. Besides the absolute necessity of self-amplification processes, the importance of energetic aspects is often underestimated. Going down to the most fundamental aspects, the distinction between a single object-that can be intrinsically asymmetric-and a collection of objects-whose racemic state is the more stable one-must be emphasized. A system of strongly interacting objects can be described as one single object retaining its individuality and a single asymmetry; weakly or non-interacting objects keep their own individuality, and are prone to racemize towards the equilibrium state. In the presence of energy fluxes, systems can be maintained in an asymmetric non-equilibrium steady-state. Such dynamical systems can retain their asymmetry for times longer than their racemization time.
Abstract: In the mean-field theory of magnetic fields, turbulent transport, i.e., the turbulent electromotive force is described by a combination of the a effect and turbulent magnetic diffusion, which are usually assumed to be proportional, respectively, to the mean field and its spatial derivatives. For a passive scalar, there is just turbulent diffusion, where the mean flux of concentration depends on the gradient of the mean concentration. However, these proportionalities are approximations that are valid only if the mean field or the mean concentration vary slowly in time. Examples are presented where turbulent transport possesses memory, i.e., where it depends crucially on the past history of the mean field. Such effects are captured by replacing turbulent transport coefficients with time integral kernels, resulting in transport coefficients that depend effectively on the frequency or the growth rate of the mean field itself. In this paper, we perform numerical experiments to find the characteristic timescale (or memory length) of this effect as well as simple analytical models of the integral kernels in the case of passive scalar concentrations and kinematic dynamos. The integral kernels can then be used to find self-consistent growth or decay rates of the mean fields. In mean-field dynamos, the growth rates and cycle periods based on steady state values of a effect, and turbulent diffusivity can be quite different from the actual values.
Abstract: Simulations of stochastically forced shear-flow turbulence in a shearing-periodic domain are used to study the spontaneous generation of large-scale flow patterns in the direction perpendicular to the plane of the shear. Based on an analysis of the resulting large-scale velocity correlations it is argued that the mechanism behind this phenomenon could be the mean-vorticity dynamo effect pioneered by Elperin, Kleeorin, and Rogachevskii [Phys. Rev. E 68, 016311 (2003)]. This effect is based on the anisotropy of the eddy viscosity tensor. One of its components may be able to replenish cross-stream mean flows by acting upon the streamwise component of the mean flow. Shear, in turn, closes the loop by acting upon the cross-stream mean flow to produce stronger streamwise mean flows. The diagonal component of the eddy viscosity is found to be of the order of the rms turbulent velocity divided by the wave number of the energy-carrying eddies.
Abstract: Aims. We study turbulent transport coefficients that describe the evolution of large-scale magnetic fields in turbulent convection. Methods. We use the test field method, together with three-dimensional numerical simulations of turbulent convection with shear and rotation, to compute turbulent transport coefficients describing the evolution of large-scale magnetic fields in mean-field theory in the kinematic regime. We employ one-dimensional mean-field models with the derived turbulent transport coefficients to examine whether they give results that are compatible with direct simulations. Results. The results for the alpha-effect as a function of rotation rate are consistent with earlier numerical studies, i.e. increasing magnitude as rotation increases and approximately cos theta latitude profile for moderate rotation. Turbulent diffusivity, eta(t), is proportional to the square of the turbulent vertical velocity in all cases. Whereas eta(t) decreases approximately inversely proportional to the wavenumber of the field, the alpha-effect and turbulent pumping show a more complex behaviour with partial or full sign changes and the magnitude staying roughly constant. In the presence of shear and no rotation, a weak alpha-effect is induced which does not seem to show any consistent trend as a function of shear rate. Provided that the shear is large enough, this small alpha-effect is able to excite a dynamo in the mean-field model. The coefficient responsible for driving the shear-current effect shows several sign changes as a function of depth but is also able to contribute to dynamo action in the mean-field model. The growth rates in these cases are, however, well below those in direct simulations, suggesting that an incoherent alpha-shear dynamo may also act in the simulations. If both rotation and shear are present, the alpha-effect is more pronounced. At the same time, the combination of the shear-current and Omega x J-effects is also stronger than in the case of shear alone, but subdominant to the alpha-shear dynamo. The results of direct simulations are consistent with mean-field models where all of these effects are taken into account without the need to invoke incoherent effects.
Abstract: The existence of large-scale dynamos in rigidly rotating turbulent convection without shear is studied using three-dimensional numerical simulations of penetrative rotating compressible convection. We demonstrate that rotating convection in a Cartesian domain can drive a large-scale dynamo even in the absence of shear. The large-scale field contains a significant fraction of the total field in the saturated state. The simulation results are compared with one-dimensional mean-field dynamo models where turbulent transport coefficients, as determined using the test field method, are used. The reason for the absence of large-scale dynamo action in earlier studies is shown to be due to the rotation being too slow: whereas the alpha-effect can change sign, its magnitude stays approximately constant as a function of rotation, and the turbulent diffusivity decreases monotonically with increasing rotation. Only when rotation is rapid enough a large-scale dynamo can be excited. The one-dimensional mean-field model with dynamo coefficients from the test-field results predicts reasonably well the dynamo excitation in the direct simulations. This result further validates the test field procedure and reinforces the interpretation that the observed dynamo is driven by a turbulent alpha-effect. This result demonstrates the existence of an alpha-effect and an alpha(2)-dynamo with natural forcing.
Abstract: Dynamo action owing to helically forced turbulence and large-scale shear is studied using direct numerical simulations. The resulting magnetic field displays propagating wave-like behavior. This behavior can be modeled in terms of an alpha Omega dynamo. In most cases super-equipartition fields are generated. By varying the fraction of helicity of the turbulence the regeneration of poloidal fields via the helicity effect (corresponding to the alpha-effect) is regulated. The saturation level of the magnetic field in the numerical models is consistent with a linear dependence on the ratio of the fractional helicities of the small and large-scale fields, as predicted by a simple nonlinear mean-field model. As the magnetic Reynolds number (Re-M) based on the wavenumber of the energy-carrying eddies is increased from 1 to 180, the cycle frequency of the large-scale field is found to decrease by a factor of about 6 in cases where the turbulence is fully helical. This is interpreted in terms of the turbulent magnetic diffusivity, which is found to be only weakly dependent on the Re M
Abstract: We analyze the mass distribution of cores formed in an isothermal, magnetized, turbulent, and self-gravitating nearly critical molecular cloud model. Cores are identified at two density threshold levels. Our main results are that the presence of self-gravity modifies the slopes of the core mass function (CMF) at the high-mass end. At low thresholds, the slope is shallower than the one predicted by pure turbulent fragmentation. The shallowness of the slope is due to the effects of core coalescence and gas accretion. Most importantly, the slope of the CMF at the high-mass end steepens when cores are selected at higher density thresholds, or alternatively, if the CMF is fitted with a lognormal function, the width of the lognormal distribution decreases with increasing threshold. This is due to the fact that gravity plays a more important role in denser structures selected at higher density threshold and leads to the conclusion that the role of gravity is essential in generating a CMF that bears more resemblance to the IMF when cores are selected with an increasing density threshold in the observations.
Abstract: The turbulent magnetic diffusivity tensor is determined in the presence of rotation or shear. The question is addressed whether dynamo action from the shear-current effect can explain large-scale magnetic field generation found in simulations with shear. For this purpose a set of evolution equations for the response to imposed test fields is solved with turbulent and mean motions calculated from the momentum and continuity equations. The corresponding results for the electromotive force are used to calculate turbulent transport coefficients. The diagonal components of the turbulent magnetic diffusivity tensor are found to be very close together, but their values increase slightly with increasing shear and decrease with increasing rotation rate. In the presence of shear, the sign of the two off-diagonal components of the turbulent magnetic diffusion tensor is the same and opposite to the sign of the shear. This implies that dynamo action from the shear-current effect is impossible, except perhaps for high magnetic Reynolds numbers. However, even though there is no alpha effect on the average, the components of the alpha tensor display Gaussian fluctuations around zero. These fluctuations are strong enough to drive an incoherent alpha-shear dynamo. The incoherent shear-current effect, on the other hand, is found to be subdominant.
Abstract: A simple explicit example of a Roberts-type dynamo is given in which the alpha effect of mean-field electrodynamics exists in spite of pointwise vanishing kinetic helicity of the fluid flow. In this way, it is shown that alpha-effect dynamos do not necessarily require nonzero kinetic helicity. A mean-field theory of Roberts-type dynamos is established within the framework of the second-order correlation approximation. In addition, numerical solutions of the original dynamo equations are given that are independent of any approximation of that kind. Both theory and numerical results demonstrate the possibility of dynamo action in the absence of kinetic helicity.
Abstract: Using numerical simulations at moderate magnetic Reynolds numbers up to 220, it is shown that in the kinematic regime, isotropic helical turbulence leads to an alpha-effect and a turbulent diffusivity whose values are independent of the magnetic Reynolds number, R-m, provided R-m exceeds unity. These turbulent coefficients are also consistent with expectations from the first-order smoothing approximation. For small values of R-m, alpha and turbulent diffusivity are proportional to R-m. Over finite time-intervals, meaningful values of alpha and turbulent diffusivity can be obtained even when there is small-scale dynamo action that produces strong magnetic fluctuations. This suggests that the fields generated by the small-scale dynamo do not make a correlated contribution to the mean electromotive force.
Abstract: Aims. To study the existence of large-scale convective dynamos under the influence of shear and rotation. Methods. Three-dimensional numerical simulations of penetrative compressible convection with uniform horizontal shear are used to study dynamo action and the generation of large-scale magnetic fields. We consider cases where the magnetic Reynolds number is either marginal or moderately supercritical with respect to small-scale dynamo action in the absence of shear and rotation. Our magnetic Reynolds number is based on the wavenumber of the depth of the convectively unstable layer. The effects of magnetic helicity fluxes are studied by comparing results for the magnetic field with open and closed boundaries. Results. Without shear no large-scale dynamos are found even if the ingredients necessary for the alpha-effect (rotation and stratification) are present in the system. When uniform horizontal shear is added, a large-scale magnetic field develops, provided the boundaries are open. In this case the mean magnetic field contains a significant fraction of the total field. For those runs where the magnetic Reynolds number is between 60 and 250, an additional small-scale dynamo is expected to be excited, but the field distribution is found to be similar to cases with smaller magnetic Reynolds number where the small-scale dynamo is not excited. In the case of closed (perfectly conducting) boundaries, magnetic helicity fluxes are suppressed and no large-scale fields are found. Similarly, poor large-scale field development is seen when vertical shear is used in combination with periodic boundary conditions in the horizontal directions. If, however, open (normal-field) boundary conditions are used in the x-direction, a large-scale field develops. These results support the notion that shear not only helps to generate the field, but it also plays a crucial role in driving magnetic helicity fluxes out of the system along the isocontours of shear, thereby allowing efficient dynamo action.
Abstract: We introduce on/off intermittency into a mean field dynamo model by imposing stochastic fluctuations in either the alpha effect or through the inclusion of a fluctuating electromotive force. Sufficiently strong small scale fluctuations with time scales of the order of 0.3-3 years can produce long term variations in the system on time scales of the order of hundreds of years. However, global suppression of magnetic activity in both hemispheres at once was not observed. The variation of the magnetic field does not resemble that of the sunspot number, but is more reminiscent of the 10 Be record. The interpretation of our results focuses attention on the connection between the level of magnetic activity and the sunspot number, an issue that must be elucidated if long term solar effects are to be well understood. (C) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Abstract: Aims. We determine the alpha effect and turbulent magnetic diffusivity for mean magnetic fields with profiles of different length scales from simulations of isotropic turbulence. We then relate these results to nonlocal formulations in which alpha and the turbulent magnetic diffusivity correspond to integral kernels. Methods. We solve evolution equations for magnetic fields that give the response to imposed test fields. These test fields correspond to mean fields with various wavenumbers. Both an imposed fully helical steady flow consisting of a pattern of screw-like motions (Roberts flow) and time-dependent, statistically steady isotropic turbulence are considered. In the latter case the evolution equations are solved simultaneously with the momentum and continuity equations. The corresponding results for the electromotive force are used to calculate alpha and magnetic diffusivity tensors. Results. For both, the Roberts flow under the second-order correlation approximation and the isotropic turbulence alpha and turbulent magnetic diffusivity are greatest on large scales and these values diminish toward smaller scales. In both cases, the alpha effect and turbulent diffusion kernels are approximated by exponentials, corresponding to Lorentzian profiles in Fourier space. For isotropic turbulence, the turbulent diffusion kernel is half as wide as the alpha effect kernel. For the Roberts flow beyond the second-order correlation approximation, the turbulent diffusion kernel becomes negative on large scales.
Abstract: In an attempt to model the accretion on to a neutron star in low-mass X-ray binaries, we present 2D hydrodynamical models of the gas flow in close vicinity of the stellar surface. First, we consider a gas pressure-dominated case, assuming that the star is non-rotating. For the stellar mass we take M-star = 1.4 x 10(-2) M-circle dot and for the gas temperature T = 5 x 10(6) K. Our results are qualitatively different in the case of a realistic neutron star mass and a realistic gas temperature of T similar or equal to 10(8) K, when the radiation pressure dominates. We show that to get the stationary solution in a latter case, the star most probably has to rotate with the considerable velocity.
Abstract: Context. The solar magnetic activity and cycle are linked to an internal dynamo. Numerical simulations are an efficient and accurate tool to investigate such intricate dynamical processes. Aims. We present the results of an international numerical benchmark study based on two-dimensional axisymmetric mean field solar dynamo models in spherical geometry. The purpose of this work is to provide reference cases that can be analyzed in detail and that can help in further development and validation of numerical codes that solve such kinematic problems. Methods. The results of eight numerical codes solving the induction equation in the framework of mean field theory are compared for three increasingly computationally intensive models of the solar dynamo: an alpha Omega dynamo with constant magnetic diffusivity, an alpha Omega dynamo with magnetic diffusivity sharply varying with depth and an example of a flux-transport Babcock-Leighton dynamo which includes a non-local source term and one large single cell of meridional circulation per hemisphere. All cases include a realistic profile of differential rotation and thus a sharp tachocline. Results. The most important finding of this study is that all codes agree quantitatively to within less than a percent for the a. dynamo cases and within a few percent for the flux-transport case. Both the critical dynamo numbers for the onset of dynamo action and the corresponding cycle periods are reasonably well recovered by all codes. Detailed comparisons of butterfly diagrams and specific cuts of both toroidal and poloidal fields at given latitude and radius confirm the good quantitative agreement. Conclusions. We believe that such a benchmark study will be a very useful tool since it provides detailed standard cases for comparison and reference.
Abstract: Aspects of turbulence in protostellar accretion discs are being reviewed. The emergence of dead zones due to poor ionization and alternatives to the magneto-rotational instability are discussed. The coupling between dust and gas in protostellar accretion discs is explained and the turbulent drag is compared with laminar drag in the Stokes and Epstein regimes. Finally, the significance of magnetic-field generation in turbulent discs is emphasized in connection with driving outflows and with star-disc coupling.
Abstract: Using direct simulations, weakly non-linear theory and non-linear mean-field theory, it is shown that the quenched velocity field of a saturated non-linear dynamo can itself act as a kinematic dynamo. The flow is driven by a forcing function that would produce a Roberts flow in the absence of a magnetic field. This result confirms an analogous finding by Cattaneo & Tobias for the more complicated case of turbulent convection, suggesting that this may be a common property of non-linear dynamos; see also the talk given online at the Kavli Institute for Theoretical Physics (http://online.kitp.ucsb.edu/online/dynamo_c08/cattaneo). It is argued that this property can be used to test non-linear mean-field dynamo theories.
Abstract: The role of shear in alleviating catastrophic quenching by shedding small-scale magnetic helicity through fluxes along contours of constant shear is discussed. The level of quenching of the dynamo effect depends on the quenched value of the turbulent magnetic diffusivity. Earlier estimates that might have suffered from the force-free degeneracy of Beltrami fields are now confirmed for shear flows where this degeneracy is lifted. For a dynamo that is saturated near equipartition field strength those estimates result in a 5-fold decrease of the magnetic diffusivity as the magnetic Reynolds number based on the wavenumber of the energy-carrying eddies is increased from 2 to 600. Finally, the role of shear in driving turbulence and large-scale fields by the magneto-rotational instability is emphasized. New simulations are presented and the 3 pi/4 phase shift between poloidal and toroidal fields is confirmed. It is suggested that this phase shift might be a useful diagnostic tool in identifying mean-field dynamo action in simulations and to distinguish this from other scenarios invoking magnetic buoyancy as a means to explain migration away from the midplane. (C) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Abstract: Aims. We determine the components of the Lambda-effect tensor that quantifies the contributions to the turbulent momentum transport even for uniform rotation. Methods. Three-dimensional numerical simulations are used to study turbulent transport in triply periodic cubes under the influence of rotation and anisotropic forcing. Comparison is made with analytical results obtained via the so-called minimal tau-approximation. Results. In the case where the turbulence intensity in the vertical direction dominates, the vertical stress is always negative. This situation is expected to occur in stellar convection zones. The horizontal component of the stress is weaker and exhibits a maximum at latitude 30 degrees - regardless of how rapid the rotation is. The minimal tau-approximation captures many of the qualitative features of the numerical results, provided the relaxation time tau is close to the turnover time, i.e. the Strouhal number is of order unity.
Abstract: The effect of a dynamo-generated mean magnetic field of Beltrami type on the mean electromotive force is studied. In the absence of the mean magnetic field the turbulence is assumed to be homogeneous and isotropic, but it becomes inhomogeneous and anisotropic with this field. Using the test-field method the dependence of the a and turbulent diffusivity tensors on the magnetic Reynolds number Re-M is determined for magnetic fields that Re M have reached approximate equipartition with the velocity field. The tensor components are characterized by a pseudoscalar alpha and a scalar turbulent magnetic diffusivity eta(t). Increasing Re-M from 2 to 600 reduces eta(t) by a factor approximate to 5, suggesting that the quenching of is, in contrast to the two-dimensional case, only weakly dependent on Re-M. Over the same range of Re-M, however, a is reduced by a factor approximate to 14, which can be explained by a corresponding Re Re increase of a magnetic contribution to the alpha-effect with opposite sign. Within this framework, the corresponding kinetic contribution to the alpha-effect turns out to be independent of Re-M for 2 <= Re-M <= 600. The level of fluctuations of alpha and eta(t) is only 10% and 20% of the respective kinematic reference values.
Abstract: The turbulent magnetic diffusivity tensor is determined in the presence of rotation or shear. The question is addressed whether dynamo action from the shear-current effect can explain large-scale magnetic field generation found in simulations with shear. For this purpose a set of evolution equations for the response to imposed test fields is solved with turbulent and mean motions calculated from the momentum and continuity equations. The corresponding results for the electromotive force are used to calculate turbulent transport coefficients. The diagonal components of the turbulent magnetic diffusivity tensor are found to be very close together, but their values increase slightly with increasing shear and decrease with increasing rotation rate. In the presence of shear, the sign of the two off-diagonal components of the turbulent magnetic diffusion tensor is the same and opposite to the sign of the shear. This implies that dynamo action from the shear-current effect is impossible, except perhaps for high magnetic Reynolds numbers. However, even though there is no alpha effect on the average, the components of the alpha tensor display Gaussian fluctuations around zero. These fluctuations are strong enough to drive an incoherent alpha-shear dynamo. The incoherent shear-current effect, on the other hand, is found to be subdominant.
Abstract: We analyze the mass distribution of cores formed in an isothermal, magnetized, turbulent, and self-gravitating nearly critical molecular cloud model. Cores are identified at two density threshold levels. Our main results are that the presence of self-gravity modifies the slopes of the core mass function (CMF) at the high-mass end. At low thresholds, the slope is shallower than the one predicted by pure turbulent fragmentation. The shallowness of the slope is due to the effects of core coalescence and gas accretion. Most importantly, the slope of the CMF at the high-mass end steepens when cores are selected at higher density thresholds, or alternatively, if the CMF is fitted with a lognormal function, the width of the lognormal distribution decreases with increasing threshold. This is due to the fact that gravity plays a more important role in denser structures selected at higher density threshold and leads to the conclusion that the role of gravity is essential in generating a CMF that bears more resemblance to the IMF when cores are selected with an increasing density threshold in the observations.
Abstract: The role of shear in alleviating catastrophic quenching by shedding small-scale magnetic helicity through fluxes along contours of constant shear is discussed. The level of quenching of the dynamo effect depends on the quenched value of the turbulent magnetic diffusivity. Earlier estimates that might have suffered from the force-free degeneracy of Beltrami fields are now confirmed for shear flows where this degeneracy is lifted. For a dynamo that is saturated near equipartition field strength those estimates result in a 5-fold decrease of the magnetic diffusivity as the magnetic Reynolds number based on the wavenumber of the energy-carrying eddies is increased from 2 to 600. Finally, the role of shear in driving turbulence and large-scale fields by the magneto-rotational instability is emphasized. New simulations are presented and the 3 pi/4 phase shift between poloidal and toroidal fields is confirmed. It is suggested that this phase shift might be a useful diagnostic tool in identifying mean-field dynamo action in simulations and to distinguish this from other scenarios invoking magnetic buoyancy as a means to explain migration away from the midplane. (C) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Abstract: Using numerical simulations at moderate magnetic Reynolds numbers up to 220, it is shown that in the kinematic regime, isotropic helical turbulence leads to an alpha-effect and a turbulent diffusivity whose values are independent of the magnetic Reynolds number, R-m, provided R-m exceeds unity. These turbulent coefficients are also consistent with expectations from the first-order smoothing approximation. For small values of R-m, alpha and turbulent diffusivity are proportional to R-m. Over finite time-intervals, meaningful values of alpha and turbulent diffusivity can be obtained even when there is small-scale dynamo action that produces strong magnetic fluctuations. This suggests that the fields generated by the small-scale dynamo do not make a correlated contribution to the mean electromotive force.
Abstract: A simple explicit example of a Roberts-type dynamo is given in which the alpha effect of mean-field electrodynamics exists in spite of pointwise vanishing kinetic helicity of the fluid flow. In this way, it is shown that alpha-effect dynamos do not necessarily require nonzero kinetic helicity. A mean-field theory of Roberts-type dynamos is established within the framework of the second-order correlation approximation. In addition, numerical solutions of the original dynamo equations are given that are independent of any approximation of that kind. Both theory and numerical results demonstrate the possibility of dynamo action in the absence of kinetic helicity.
Abstract: Aims. We determine the components of the Lambda-effect tensor that quantifies the contributions to the turbulent momentum transport even for uniform rotation. Methods. Three-dimensional numerical simulations are used to study turbulent transport in triply periodic cubes under the influence of rotation and anisotropic forcing. Comparison is made with analytical results obtained via the so-called minimal tau-approximation. Results. In the case where the turbulence intensity in the vertical direction dominates, the vertical stress is always negative. This situation is expected to occur in stellar convection zones. The horizontal component of the stress is weaker and exhibits a maximum at latitude 30 degrees - regardless of how rapid the rotation is. The minimal tau-approximation captures many of the qualitative features of the numerical results, provided the relaxation time tau is close to the turnover time, i.e. the Strouhal number is of order unity.
Abstract: Aims. To study the existence of large-scale convective dynamos under the influence of shear and rotation. Methods. Three-dimensional numerical simulations of penetrative compressible convection with uniform horizontal shear are used to study dynamo action and the generation of large-scale magnetic fields. We consider cases where the magnetic Reynolds number is either marginal or moderately supercritical with respect to small-scale dynamo action in the absence of shear and rotation. Our magnetic Reynolds number is based on the wavenumber of the depth of the convectively unstable layer. The effects of magnetic helicity fluxes are studied by comparing results for the magnetic field with open and closed boundaries. Results. Without shear no large-scale dynamos are found even if the ingredients necessary for the alpha-effect (rotation and stratification) are present in the system. When uniform horizontal shear is added, a large-scale magnetic field develops, provided the boundaries are open. In this case the mean magnetic field contains a significant fraction of the total field. For those runs where the magnetic Reynolds number is between 60 and 250, an additional small-scale dynamo is expected to be excited, but the field distribution is found to be similar to cases with smaller magnetic Reynolds number where the small-scale dynamo is not excited. In the case of closed (perfectly conducting) boundaries, magnetic helicity fluxes are suppressed and no large-scale fields are found. Similarly, poor large-scale field development is seen when vertical shear is used in combination with periodic boundary conditions in the horizontal directions. If, however, open (normal-field) boundary conditions are used in the x-direction, a large-scale field develops. These results support the notion that shear not only helps to generate the field, but it also plays a crucial role in driving magnetic helicity fluxes out of the system along the isocontours of shear, thereby allowing efficient dynamo action.
Abstract: Using direct simulations, weakly non-linear theory and non-linear mean-field theory, it is shown that the quenched velocity field of a saturated non-linear dynamo can itself act as a kinematic dynamo. The flow is driven by a forcing function that would produce a Roberts flow in the absence of a magnetic field. This result confirms an analogous finding by Cattaneo & Tobias for the more complicated case of turbulent convection, suggesting that this may be a common property of non-linear dynamos; see also the talk given online at the Kavli Institute for Theoretical Physics (http://online.kitp.ucsb.edu/online/dynamo_c08/cattaneo). It is argued that this property can be used to test non-linear mean-field dynamo theories.
Abstract: In an attempt to model the accretion on to a neutron star in low-mass X-ray binaries, we present 2D hydrodynamical models of the gas flow in close vicinity of the stellar surface. First, we consider a gas pressure-dominated case, assuming that the star is non-rotating. For the stellar mass we take M-star = 1.4 x 10(-2) M-circle dot and for the gas temperature T = 5 x 10(6) K. Our results are qualitatively different in the case of a realistic neutron star mass and a realistic gas temperature of T similar or equal to 10(8) K, when the radiation pressure dominates. We show that to get the stationary solution in a latter case, the star most probably has to rotate with the considerable velocity.
Abstract: Aspects of turbulence in protostellar accretion discs are being reviewed. The emergence of dead zones due to poor ionization and alternatives to the magneto-rotational instability are discussed. The coupling between dust and gas in protostellar accretion discs is explained and the turbulent drag is compared with laminar drag in the Stokes and Epstein regimes. Finally, the significance of magnetic-field generation in turbulent discs is emphasized in connection with driving outflows and with star-disc coupling.
Abstract: A simple explicit example of a Roberts-type dynamo is given in which the alpha effect of mean-field electrodynamics exists in spite of pointwise vanishing kinetic helicity of the fluid flow. In this way, it is shown that alpha-effect dynamos do not necessarily require nonzero kinetic helicity. A mean-field theory of Roberts-type dynamos is established within the framework of the second-order correlation approximation. In addition, numerical solutions of the original dynamo equations are given that are independent of any approximation of that kind. Both theory and numerical results demonstrate the possibility of dynamo action in the absence of kinetic helicity.
Abstract: The effect of a dynamo-generated mean magnetic field of Beltrami type on the mean electromotive force is studied. In the absence of the mean magnetic field the turbulence is assumed to be homogeneous and isotropic, but it becomes inhomogeneous and anisotropic with this field. Using the test-field method the dependence of the a and turbulent diffusivity tensors on the magnetic Reynolds number Re-M is determined for magnetic fields that Re M have reached approximate equipartition with the velocity field. The tensor components are characterized by a pseudoscalar alpha and a scalar turbulent magnetic diffusivity eta(t). Increasing Re-M from 2 to 600 reduces eta(t) by a factor approximate to 5, suggesting that the quenching of is, in contrast to the two-dimensional case, only weakly dependent on Re-M. Over the same range of Re-M, however, a is reduced by a factor approximate to 14, which can be explained by a corresponding Re Re increase of a magnetic contribution to the alpha-effect with opposite sign. Within this framework, the corresponding kinetic contribution to the alpha-effect turns out to be independent of Re-M for 2 <= Re-M <= 600. The level of fluctuations of alpha and eta(t) is only 10% and 20% of the respective kinematic reference values.
Abstract: Context. The solar magnetic activity and cycle are linked to an internal dynamo. Numerical simulations are an efficient and accurate tool to investigate such intricate dynamical processes. Aims. We present the results of an international numerical benchmark study based on two-dimensional axisymmetric mean field solar dynamo models in spherical geometry. The purpose of this work is to provide reference cases that can be analyzed in detail and that can help in further development and validation of numerical codes that solve such kinematic problems. Methods. The results of eight numerical codes solving the induction equation in the framework of mean field theory are compared for three increasingly computationally intensive models of the solar dynamo: an alpha Omega dynamo with constant magnetic diffusivity, an alpha Omega dynamo with magnetic diffusivity sharply varying with depth and an example of a flux-transport Babcock-Leighton dynamo which includes a non-local source term and one large single cell of meridional circulation per hemisphere. All cases include a realistic profile of differential rotation and thus a sharp tachocline. Results. The most important finding of this study is that all codes agree quantitatively to within less than a percent for the a. dynamo cases and within a few percent for the flux-transport case. Both the critical dynamo numbers for the onset of dynamo action and the corresponding cycle periods are reasonably well recovered by all codes. Detailed comparisons of butterfly diagrams and specific cuts of both toroidal and poloidal fields at given latitude and radius confirm the good quantitative agreement. Conclusions. We believe that such a benchmark study will be a very useful tool since it provides detailed standard cases for comparison and reference.
Abstract: Aims. We determine the alpha effect and turbulent magnetic diffusivity for mean magnetic fields with profiles of different length scales from simulations of isotropic turbulence. We then relate these results to nonlocal formulations in which alpha and the turbulent magnetic diffusivity correspond to integral kernels. Methods. We solve evolution equations for magnetic fields that give the response to imposed test fields. These test fields correspond to mean fields with various wavenumbers. Both an imposed fully helical steady flow consisting of a pattern of screw-like motions (Roberts flow) and time-dependent, statistically steady isotropic turbulence are considered. In the latter case the evolution equations are solved simultaneously with the momentum and continuity equations. The corresponding results for the electromotive force are used to calculate alpha and magnetic diffusivity tensors. Results. For both, the Roberts flow under the second-order correlation approximation and the isotropic turbulence alpha and turbulent magnetic diffusivity are greatest on large scales and these values diminish toward smaller scales. In both cases, the alpha effect and turbulent diffusion kernels are approximated by exponentials, corresponding to Lorentzian profiles in Fourier space. For isotropic turbulence, the turbulent diffusion kernel is half as wide as the alpha effect kernel. For the Roberts flow beyond the second-order correlation approximation, the turbulent diffusion kernel becomes negative on large scales.
Abstract: We introduce on/off intermittency into a mean field dynamo model by imposing stochastic fluctuations in either the alpha effect or through the inclusion of a fluctuating electromotive force. Sufficiently strong small scale fluctuations with time scales of the order of 0.3-3 years can produce long term variations in the system on time scales of the order of hundreds of years. However, global suppression of magnetic activity in both hemispheres at once was not observed. The variation of the magnetic field does not resemble that of the sunspot number, but is more reminiscent of the 10 Be record. The interpretation of our results focuses attention on the connection between the level of magnetic activity and the sunspot number, an issue that must be elucidated if long term solar effects are to be well understood. (C) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Abstract: The motivation for considering distributed large scale dynamos in the solar context is reviewed in connection with the magnetic helicity constraint. Preliminary accounts of 3-dimensional direct numerical simulations (in spherical shell segments) and simulations of 2-dimensional mean field models (in spherical shells) are presented. Interesting similarities as well as some differences are noted. (C) 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Abstract: The thermal instability with a piecewise power law cooling function is investigated using one- and three-dimensional simulations with periodic and shearing-periodic boundary conditions in the presence of constant thermal diffusion and kinematic viscosity coefficients. Consistent with earlier findings, the flow behavior depends on the average density, [rho]. When [rho] is in the range (1-5); 10(-24) g cm(-3), the system is unstable and segregates into cool and warm phases with temperatures of roughly 100 and 10(4) K, respectively. However, in all cases the resulting average pressure [p] is independent of [rho] and just a little above the minimum value. For a constant heating rate of 0.015 ergs g(-1) s(-1), the mean pressure is around 24 x 10(-14) dyn (corresponding to p/ k(B) approximate to 1750 K cm(-3)). Cool patches tend to coalesce into bigger ones. In all cases investigated, there is no sustained turbulence, which is in agreement with earlier results. Simulations in which turbulence is driven by a body force show that when rms velocities of between 10 and 30 km s(-1) are obtained, the resulting dissipation rates are comparable to the thermal energy input rate. The resulting mean pressures are then about 30 x 10(-14) dyn, corresponding to p/k(B) approximate to 2170 K cm(-3). This is comparable to the value expected for the Galaxy. Differential rotation tends to make the flow two-dimensional, that is, uniform in the streamwise direction, but this does not lead to instability.
Abstract: Homogeneous anisotropic turbulence simulations are used to determine off-diagonal components of the Reynolds stress tensor and its parameterization in terms of turbulent viscosity and A-effect. The turbulence is forced in an anisotropic fashion by enhancing the strength of the forcing in the vertical direction. The Coriolis force is included with a rotation axis inclined relative to the vertical direction. The system studied here is significantly simpler than that of turbulent stratified convection which has often been used to study Reynolds stresses. Certain puzzling features of the results for convection, such as sign changes or highly concentrated latitude distributions, are not present in the simpler system considered here. (c) 2007 WILEY VCH Verlag GmbH & Co. KGaA, Weinheim.
Abstract: Homogeneous anisotropic turbulence simulations are used to determine off-diagonal components of the Reynolds stress tensor and its parameterization in terms of turbulent viscosity and A-effect. The turbulence is forced in an anisotropic fashion by enhancing the strength of the forcing in the vertical direction. The Coriolis force is included with a rotation axis inclined relative to the vertical direction. The system studied here is significantly simpler than that of turbulent stratified convection which has often been used to study Reynolds stresses. Certain puzzling features of the results for convection, such as sign changes or highly concentrated latitude distributions, are not present in the simpler system considered here. (c) 2007 WILEY VCH Verlag GmbH & Co. KGaA, Weinheim.
Abstract: The backreaction of the Lorentz force on the alpha-effect is studied in the limit of small magnetic and fluid Reynolds numbers, using the first-order smoothing approximation (FOSA) to solve both the induction and momentum equations. Both steady and time-dependent forcings are considered. In the low Reynolds number limit, the velocity and magnetic fields can be expressed explicitly in terms of the forcing function. The non-linear alpha-effect is then shown to be expressible in several equivalent forms in agreement with formalisms that are used in various closure schemes. On one hand, one can express alpha completely in terms of the helical properties of the velocity field as in traditional FOSA, or, alternatively, as the sum of two terms, a so-called kinetic alpha-effect and an oppositely signed term proportional to the helical part of the small-scale magnetic field. These results hold for both steady and time-dependent forcing at arbitrary strength of the mean field. In addition, the tau-approximation is considered in the limit of small fluid and magnetic Reynolds numbers. In this limit, the tau closure term is absent and the viscous and resistive terms must be fully included. The underlying equations are then identical to those used under FOSA, but they reveal interesting differences between the steady and time-dependent forcing. For steady forcing, the correlation between the forcing function and the small-scale magnetic field turns out to contribute in a crucial manner to determine the net alpha-effect. However for delta-correlated time-dependent forcing, this force-field correlation vanishes, enabling one to write alpha exactly as the sum of kinetic and magnetic alpha-effects, similar to what one obtains also in the large Reynolds number regime in the tau-approximation closure hypothesis. In the limit of strong imposed fields, B-0, we find alpha proportional to B-0(-2) for delta-correlated forcing, in contrast to the well-known alpha proportional to B-0(-3) behaviour for the case of a steady forcing. The analysis presented here is also shown to be in agreement with numerical simulations of steady as well as random helical flows.
Abstract: A recently proposed model of non-autocatalytic reactions in dipeptide formation that leads to spontaneous symmetry breaking and homochirality was examined. The model is governed by activation, polymerization, epimerization, and depolymerization of amino acids. Symmetry breaking was determined to result primarily from the different rates of reactions that involve homodimers and heterodimers, i.e., stereoselective reactions, and the fact that epimerization can only occur on the N-terminal residue and not on the C-terminal residue. This corresponds to an auto-inductive cyclic process that works only in one direction. It is argued that epimerization mimics autocatalytic behavior as well as mutual antagonism, both of which are known to be crucial for the production of full homochirality.
Abstract: The backreaction of the Lorentz force on the alpha-effect is studied in the limit of small magnetic and fluid Reynolds numbers, using the first-order smoothing approximation (FOSA) to solve both the induction and momentum equations. Both steady and time-dependent forcings are considered. In the low Reynolds number limit, the velocity and magnetic fields can be expressed explicitly in terms of the forcing function. The non-linear alpha-effect is then shown to be expressible in several equivalent forms in agreement with formalisms that are used in various closure schemes. On one hand, one can express alpha completely in terms of the helical properties of the velocity field as in traditional FOSA, or, alternatively, as the sum of two terms, a so-called kinetic alpha-effect and an oppositely signed term proportional to the helical part of the small-scale magnetic field. These results hold for both steady and time-dependent forcing at arbitrary strength of the mean field. In addition, the tau-approximation is considered in the limit of small fluid and magnetic Reynolds numbers. In this limit, the tau closure term is absent and the viscous and resistive terms must be fully included. The underlying equations are then identical to those used under FOSA, but they reveal interesting differences between the steady and time-dependent forcing. For steady forcing, the correlation between the forcing function and the small-scale magnetic field turns out to contribute in a crucial manner to determine the net alpha-effect. However for delta-correlated time-dependent forcing, this force-field correlation vanishes, enabling one to write alpha exactly as the sum of kinetic and magnetic alpha-effects, similar to what one obtains also in the large Reynolds number regime in the tau-approximation closure hypothesis. In the limit of strong imposed fields, B-0, we find alpha proportional to B-0(-2) for delta-correlated forcing, in contrast to the well-known alpha proportional to B-0(-3) behaviour for the case of a steady forcing. The analysis presented here is also shown to be in agreement with numerical simulations of steady as well as random helical flows.
Abstract: The thermal instability with a piecewise power law cooling function is investigated using one- and three-dimensional simulations with periodic and shearing-periodic boundary conditions in the presence of constant thermal diffusion and kinematic viscosity coefficients. Consistent with earlier findings, the flow behavior depends on the average density, [rho]. When [rho] is in the range (1-5); 10(-24) g cm(-3), the system is unstable and segregates into cool and warm phases with temperatures of roughly 100 and 10(4) K, respectively. However, in all cases the resulting average pressure [p] is independent of [rho] and just a little above the minimum value. For a constant heating rate of 0.015 ergs g(-1) s(-1), the mean pressure is around 24 x 10(-14) dyn (corresponding to p/ k(B) approximate to 1750 K cm(-3)). Cool patches tend to coalesce into bigger ones. In all cases investigated, there is no sustained turbulence, which is in agreement with earlier results. Simulations in which turbulence is driven by a body force show that when rms velocities of between 10 and 30 km s(-1) are obtained, the resulting dissipation rates are comparable to the thermal energy input rate. The resulting mean pressures are then about 30 x 10(-14) dyn, corresponding to p/k(B) approximate to 2170 K cm(-3). This is comparable to the value expected for the Galaxy. Differential rotation tends to make the flow two-dimensional, that is, uniform in the streamwise direction, but this does not lead to instability.
Abstract: A recently proposed model of non-autocatalytic reactions in dipeptide formation that leads to spontaneous symmetry breaking and homochirality was examined. The model is governed by activation, polymerization, epimerization, and depolymerization of amino acids. Symmetry breaking was determined to result primarily from the different rates of reactions that involve homodimers and heterodimers, i.e., stereoselective reactions, and the fact that epimerization can only occur on the N-terminal residue and not on the C-terminal residue. This corresponds to an auto-inductive cyclic process that works only in one direction. It is argued that epimerization mimics autocatalytic behavior as well as mutual antagonism, both of which are known to be crucial for the production of full homochirality.
Abstract: Magnetic helicity effects are discussed in laboratory and astrophysical settings. Firstly, dynamo action in Taylor-Green flows is discussed for different boundary conditions. However, because of the lack of scale separation with respect to the container, no large-scale field is being produced and there is no resistively slow saturation phase as otherwise expected. Secondly, the build-up of a large-scale field is demonstrated in a simulation where a localized magnetic eddy produces field on a larger scale if the eddy possesses a swirl. Such a set-up might be realizable experimentally through coils. Finally, new emerging issues regarding the connection between magnetic helicity and the solar dynamo are discussed. It is demonstrated that dynamos with a nonlocal ( Babcock-Leighton type) a effect can also be catastrophically quenched, unless there are magnetic helicity fluxes.
Abstract: Using simulations of isotropically forced helical turbulence the contributions to kinetic and magnetic alpha effects are computed. It is shown that for the parameter regimes considered in an earlier publication (Brandenburg & Subramanian 2005), the expressions for isotropic and anisotropic alpha effects give quantitatively similar results. Both kinetic and magnetic alpha effects are proportional to a relaxation time whose value, in units of the turnover time, is shown to be approximately unity and independent of the magnetic Reynolds number. (c) 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Abstract: Magnetic helicity effects are discussed in laboratory and astrophysical settings. Firstly, dynamo action in Taylor-Green flows is discussed for different boundary conditions. However, because of the lack of scale separation with respect to the container, no large-scale field is being produced and there is no resistively slow saturation phase as otherwise expected. Secondly, the build-up of a large-scale field is demonstrated in a simulation where a localized magnetic eddy produces field on a larger scale if the eddy possesses a swirl. Such a set-up might be realizable experimentally through coils. Finally, new emerging issues regarding the connection between magnetic helicity and the solar dynamo are discussed. It is demonstrated that dynamos with a nonlocal ( Babcock-Leighton type) a effect can also be catastrophically quenched, unless there are magnetic helicity fluxes.
Abstract: A recently proposed model of non-autocatalytic reactions in dipeptide formation that leads to spontaneous symmetry breaking and homochirality was examined. The model is governed by activation, polymerization, epimerization, and depolymerization of amino acids. Symmetry breaking was determined to result primarily from the different rates of reactions that involve homodimers and heterodimers, i.e., stereoselective reactions, and the fact that epimerization can only occur on the N-terminal residue and not on the C-terminal residue. This corresponds to an auto-inductive cyclic process that works only in one direction. It is argued that epimerization mimics autocatalytic behavior as well as mutual antagonism, both of which are known to be crucial for the production of full homochirality.
Abstract: Using simulations of isotropically forced helical turbulence the contributions to kinetic and magnetic alpha effects are computed. It is shown that for the parameter regimes considered in an earlier publication (Brandenburg & Subramanian 2005), the expressions for isotropic and anisotropic alpha effects give quantitatively similar results. Both kinetic and magnetic alpha effects are proportional to a relaxation time whose value, in units of the turnover time, is shown to be approximately unity and independent of the magnetic Reynolds number. (c) 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Abstract: The motivation for considering distributed large scale dynamos in the solar context is reviewed in connection with the magnetic helicity constraint. Preliminary accounts of 3-dimensional direct numerical simulations (in spherical shell segments) and simulations of 2-dimensional mean field models (in spherical shells) are presented. Interesting similarities as well as some differences are noted. (C) 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Abstract: Magnetohydrodynamic simulations of fully convective, rotating spheres with volume heating near the center and cooling at the surface are presented. The dynamo-generated magnetic field saturates at equipartition field strength near the surface. In the interior, the field is dominated by small-scale structures, but outside the sphere, by the global scale. Azimuthal averages of the field reveal a large-scale field of smaller amplitude also inside the star. The internal angular velocity shows some tendency to be constant along cylinders and is "antisolar'' (fastest at the poles and slowest at the equator).
Abstract: Aims. An efficient algorithm for calculating radiative transfer on massively parallel computers using domain decomposition is presented. Methods. The integral formulation of the transfer equation is used to divide the problem into a local but compute-intensive part for calculating the intensity and optical depth integrals, and a nonlocal part for communicating the intensity between adjacent processors. Results. The waiting time of idle processors during the nonlocal communication part does not have a severe impact on the scaling. The wall clock time thus scales nearly linearly with the inverse number of processors.
Abstract: Star-disc coupling is considered in numerical models where the stellar field is not an imposed perfect dipole, but instead a more irregular self-adjusting dynamo-generated field. Using axisymmetric simulations of the hydromagnetic mean-field equations, it is shown that the resulting stellar field configuration is more complex, but significantly better suited for driving a stellar wind. In agreement with recent findings by a number of people, star-disc coupling is less efficient in braking the star than previously thought. Moreover, stellar wind braking becomes equally important. In contrast to a perfect stellar dipole field, dynamo-generated stellar fields favor field-aligned accretion with considerably higher velocity at low latitudes, where the field is weaker and originating in the disc. Accretion is no longer nearly periodic (as it is in the case of a stellar dipole), but it is more irregular and episodic.
Abstract: Aims. Nonlinear behaviour of galactic dynamos is studied, allowing for magnetic helicity removal by the galactic fountain flow. Methods. A suitable advection speed is estimated, and a one-dimensional mean-field dynamo model with dynamic alpha-effect is explored. Results. It is shown that the galactic fountain flow is efficient in removing magnetic helicity from galactic discs. This alleviates the constraint on the galactic mean-field dynamo re resulting from magnetic helicity conservation and thereby allows the mean magnetic field to saturate at strength comparable to equipartition with the turbulent kinetic energy.
Abstract: In an attempt to determine the outer scale of turbulence driven by localized sources, such as supernova explosions in the interstellar medium, we consider a forcing function given by the gradient of Gaussian profiles localized at random positions. Different coherence times of the forcing function are considered. In order to isolate the effects specific to the nature of the forcing function, we consider the case of a polytropic equation of state and restrict ourselves to forcing amplitudes such that the flow remains subsonic. When the coherence time is short, the outer scale agrees with the half-width of the Gaussian. Longer coherence times can cause extra power at large scales, but this would not yield power-law behaviour at scales larger than that of the expansion waves. At scales smaller than the scale of the expansion waves the spectrum is close to power law with a spectral exponent of -2. The resulting flow is virtually free of vorticity. Viscous driving of vorticity turns out to be weak and self-amplification through the non-linear term is found to be insignificant. No evidence for small-scale dynamo action is found in cases where the magnetic induction equation is solved simultaneously with the other equations.
Abstract: Aims. To study turbulence in the Orion Molecular Cloud (OMC1) by comparing observed and simulated characteristics of the gas motions. Methods. Using a dataset of vibrationally excited H-2 emission in OMC1 containing radial velocity and brightness which covers scales from 70 AU to 30 000 AU, we present the structure functions and the scaling of the structure functions with their order. These are compared with the predictions of two-dimensional projections of simulations of supersonic hydrodynamic turbulence. Results. The structure functions of OMC1 are not well represented by power laws, but show clear deviations below 2000 AU. However, using the technique of extended self-similarity, power laws are recovered at scales down to 160 AU. The scaling of the higher order structure functions with order deviates from the standard scaling for supersonic turbulence. This is explained as a selection effect of preferentially observing the shocked part of the gas and the scaling can be reproduced using line-of-sight integrated velocity data from subsets of supersonic turbulence simulations. These subsets select regions of strong flow convergence and high density associated with shock structure. Deviations of the structure functions in OMC1 from power laws cannot however be reproduced in simulations and remains an outstanding issue.
Abstract: Some common properties of helical magnetic fields in decaying and driven turbulence are discussed. These include mainly the inverse cascade that produces fields on progressively larger scales. Magnetic helicity also restricts the evolution of the large-scale field: the field decays less rapidly than a non-helical field, but it also saturates more slowly, i.e. on a resistive time scale if there are no magnetic helicity fluxes. The former effect is utilized in primordial field scenarios, while the latter is important for successfully explaining astrophysical dynamos that saturate faster than resistively. Dynamo action is argued to be important not only in the galactic dynamo, but also in accretion discs in active galactic nuclei and around protostars, both of which contribute to producing a strong enough seed magnetic field. Although primordial magnetic fields may be too weak to compete with these astrophysical mechanisms, such fields could perhaps still be important in producing polarization effects in the cosmic background radiation. (c) 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Abstract: Direct and large eddy simulations of hydrodynamic and hydromagnetic turbulence have been performed in an attempt to isolate artifacts from real and possibly asymptotic features in the energy spectra. It is shown that in a hydrodynamic turbulence simulation with a Smagorinsky subgrid scale model using 512(3) mesh points, two important features of the 4096(3) simulation on the Earth simulator [Y. Kaneda , Phys. Fluids 15, L21 (2003)] are reproduced: a k(-0.1) correction to the inertial range with a k(-5/3) Kolmogorov slope and the form of the bottleneck just before the dissipative subrange. Furthermore, it is shown that, while a Smagorinsky-type model for the induction equation causes an artificial and unacceptable reduction in the dynamo efficiency, hyper-resistivity yields good agreement with direct simulations. In the large-scale part of the inertial range, an excess of the spectral magnetic energy over the spectral kinetic energy is confirmed. However, a trend toward spectral equipartition at smaller scales in the inertial range can be identified. With magnetic fields, no explicit bottleneck effect is seen.
Abstract: A gauge-invariant and hence physically meaningful definition of magnetic helicity density for random fields is proposed, using the Gauss linking formula, as the density of correlated field line linkages. This definition is applied to the random small-scale field in weakly inhomogeneous turbulence, whose correlation length is small compared with the scale on which the turbulence varies. For inhomogeneous systems, with or without boundaries, our technique then allows one to study the local magnetic helicity density evolution in a gauge-independent fashion, which was not possible earlier. This evolution equation is governed by local sources ( owing to the mean field) and by the divergence of a magnetic helicity flux density. The role of magnetic helicity fluxes in alleviating catastrophic quenching of mean field dynamos is discussed.
Abstract: The location of the solar dynamo is discussed in the context of new insights into the theory of nonlinear turbulent dynamos. It is argued that, from a dynamo-theoretic point of view, the bottom of the convection zone is not a likely location for the solar dynamo, but that it may be distributed over the convection zone. The near surface shear layer produces not only east-west field alignment, but it also helps the dynamo to dispose of its excess small scale magnetic helicity.
Abstract: The macroscopic behaviour of cosmic rays in turbulent magnetic fields is discussed. An implementation of anisotropic diffusion of cosmic rays with respect to the magnetic field in a non-conservative, high-order, finite-difference magnetohydrodynamic code is discussed. It is shown that the standard implementation fails near singular X-points of the magnetic field, which are common if the field is random. A modification to the diffusion model for cosmic rays is described and the resulting telegraph equation (implemented by solving a dynamic equation for the diffusive flux of cosmic rays) is used; it is argued that this modification may better describe the physics of cosmic ray diffusion. The present model reproduces several processes important for the propagation and local confinement of cosmic rays, including spreading perpendicular to the local large-scale magnetic field, controlled by the random-to-total magnetic field ratio, and the balance between cosmic ray pressure and magnetic tension. Cosmic ray diffusion is discussed in the context of a random magnetic field produced by turbulent dynamo action. It is argued that energy equipartition between cosmic rays and other constituents of the interstellar medium does not necessarily imply that cosmic rays play a significant role in the balance of forces.
Abstract: Aims. To quantify the transient growth of nonaxisymmetric perturbations in unstratified magnetized and stratified non-magnetized rotating linear shear flows in the shearing sheet approximation of accretion disc flows. Methods. The Rayleigh quotient in modal approaches for the linearized equations (with time-dependent wavenumber) and the amplitudes from direct shearing sheet simulations using a finite difference code are compared. Results. Both approaches agree in their predicted growth behavior. The magneto-rotational instability for axisymmetric and non-axisymmetric perturbations is shown to have the same dependence of the (instantaneous) growth rate on the wavenumber along the magnetic field, but in the nonaxisymmetric case the growth is only transient. However, a meaningful dependence of the Rayleigh quotient on the radial wavenumber is obtained. While in the magnetized case the total amplification factor can be several orders of magnitude, it is only of order ten or less in the nonmagnetic case. Stratification is shown to have a stabilizing effect. In the present case of shearing-periodic boundaries the (local) strato-rotational instability seems to be absent.
Abstract: Aims. Nonlinear behaviour of galactic dynamos is studied, allowing for magnetic helicity removal by the galactic fountain flow. Methods. A suitable advection speed is estimated, and a one-dimensional mean-field dynamo model with dynamic alpha-effect is explored. Results. It is shown that the galactic fountain flow is efficient in removing magnetic helicity from galactic discs. This alleviates the constraint on the galactic mean-field dynamo re resulting from magnetic helicity conservation and thereby allows the mean magnetic field to saturate at strength comparable to equipartition with the turbulent kinetic energy.
Abstract: A gauge-invariant and hence physically meaningful definition of magnetic helicity density for random fields is proposed, using the Gauss linking formula, as the density of correlated field line linkages. This definition is applied to the random small-scale field in weakly inhomogeneous turbulence, whose correlation length is small compared with the scale on which the turbulence varies. For inhomogeneous systems, with or without boundaries, our technique then allows one to study the local magnetic helicity density evolution in a gauge-independent fashion, which was not possible earlier. This evolution equation is governed by local sources ( owing to the mean field) and by the divergence of a magnetic helicity flux density. The role of magnetic helicity fluxes in alleviating catastrophic quenching of mean field dynamos is discussed.
Abstract: In an attempt to determine the outer scale of turbulence driven by localized sources, such as supernova explosions in the interstellar medium, we consider a forcing function given by the gradient of Gaussian profiles localized at random positions. Different coherence times of the forcing function are considered. In order to isolate the effects specific to the nature of the forcing function, we consider the case of a polytropic equation of state and restrict ourselves to forcing amplitudes such that the flow remains subsonic. When the coherence time is short, the outer scale agrees with the half-width of the Gaussian. Longer coherence times can cause extra power at large scales, but this would not yield power-law behaviour at scales larger than that of the expansion waves. At scales smaller than the scale of the expansion waves the spectrum is close to power law with a spectral exponent of -2. The resulting flow is virtually free of vorticity. Viscous driving of vorticity turns out to be weak and self-amplification through the non-linear term is found to be insignificant. No evidence for small-scale dynamo action is found in cases where the magnetic induction equation is solved simultaneously with the other equations.
Abstract: The macroscopic behaviour of cosmic rays in turbulent magnetic fields is discussed. An implementation of anisotropic diffusion of cosmic rays with respect to the magnetic field in a non-conservative, high-order, finite-difference magnetohydrodynamic code is discussed. It is shown that the standard implementation fails near singular X-points of the magnetic field, which are common if the field is random. A modification to the diffusion model for cosmic rays is described and the resulting telegraph equation (implemented by solving a dynamic equation for the diffusive flux of cosmic rays) is used; it is argued that this modification may better describe the physics of cosmic ray diffusion. The present model reproduces several processes important for the propagation and local confinement of cosmic rays, including spreading perpendicular to the local large-scale magnetic field, controlled by the random-to-total magnetic field ratio, and the balance between cosmic ray pressure and magnetic tension. Cosmic ray diffusion is discussed in the context of a random magnetic field produced by turbulent dynamo action. It is argued that energy equipartition between cosmic rays and other constituents of the interstellar medium does not necessarily imply that cosmic rays play a significant role in the balance of forces.
Abstract: Magnetohydrodynamic simulations of fully convective, rotating spheres with volume heating near the center and cooling at the surface are presented. The dynamo-generated magnetic field saturates at equipartition field strength near the surface. In the interior, the field is dominated by small-scale structures, but outside the sphere, by the global scale. Azimuthal averages of the field reveal a large-scale field of smaller amplitude also inside the star. The internal angular velocity shows some tendency to be constant along cylinders and is "antisolar'' (fastest at the poles and slowest at the equator).
Abstract: The location of the solar dynamo is discussed in the context of new insights into the theory of nonlinear turbulent dynamos. It is argued that, from a dynamo-theoretic point of view, the bottom of the convection zone is not a likely location for the solar dynamo, but that it may be distributed over the convection zone. The near surface shear layer produces not only east-west field alignment, but it also helps the dynamo to dispose of its excess small scale magnetic helicity.
Abstract: Aims. To study turbulence in the Orion Molecular Cloud (OMC1) by comparing observed and simulated characteristics of the gas motions. Methods. Using a dataset of vibrationally excited H-2 emission in OMC1 containing radial velocity and brightness which covers scales from 70 AU to 30 000 AU, we present the structure functions and the scaling of the structure functions with their order. These are compared with the predictions of two-dimensional projections of simulations of supersonic hydrodynamic turbulence. Results. The structure functions of OMC1 are not well represented by power laws, but show clear deviations below 2000 AU. However, using the technique of extended self-similarity, power laws are recovered at scales down to 160 AU. The scaling of the higher order structure functions with order deviates from the standard scaling for supersonic turbulence. This is explained as a selection effect of preferentially observing the shocked part of the gas and the scaling can be reproduced using line-of-sight integrated velocity data from subsets of supersonic turbulence simulations. These subsets select regions of strong flow convergence and high density associated with shock structure. Deviations of the structure functions in OMC1 from power laws cannot however be reproduced in simulations and remains an outstanding issue.
Abstract: Direct and large eddy simulations of hydrodynamic and hydromagnetic turbulence have been performed in an attempt to isolate artifacts from real and possibly asymptotic features in the energy spectra. It is shown that in a hydrodynamic turbulence simulation with a Smagorinsky subgrid scale model using 512(3) mesh points, two important features of the 4096(3) simulation on the Earth simulator [Y. Kaneda , Phys. Fluids 15, L21 (2003)] are reproduced: a k(-0.1) correction to the inertial range with a k(-5/3) Kolmogorov slope and the form of the bottleneck just before the dissipative subrange. Furthermore, it is shown that, while a Smagorinsky-type model for the induction equation causes an artificial and unacceptable reduction in the dynamo efficiency, hyper-resistivity yields good agreement with direct simulations. In the large-scale part of the inertial range, an excess of the spectral magnetic energy over the spectral kinetic energy is confirmed. However, a trend toward spectral equipartition at smaller scales in the inertial range can be identified. With magnetic fields, no explicit bottleneck effect is seen.
Abstract: Star-disc coupling is considered in numerical models where the stellar field is not an imposed perfect dipole, but instead a more irregular self-adjusting dynamo-generated field. Using axisymmetric simulations of the hydromagnetic mean-field equations, it is shown that the resulting stellar field configuration is more complex, but significantly better suited for driving a stellar wind. In agreement with recent findings by a number of people, star-disc coupling is less efficient in braking the star than previously thought. Moreover, stellar wind braking becomes equally important. In contrast to a perfect stellar dipole field, dynamo-generated stellar fields favor field-aligned accretion with considerably higher velocity at low latitudes, where the field is weaker and originating in the disc. Accretion is no longer nearly periodic (as it is in the case of a stellar dipole), but it is more irregular and episodic.
Abstract: Some common properties of helical magnetic fields in decaying and driven turbulence are discussed. These include mainly the inverse cascade that produces fields on progressively larger scales. Magnetic helicity also restricts the evolution of the large-scale field: the field decays less rapidly than a non-helical field, but it also saturates more slowly, i.e. on a resistive time scale if there are no magnetic helicity fluxes. The former effect is utilized in primordial field scenarios, while the latter is important for successfully explaining astrophysical dynamos that saturate faster than resistively. Dynamo action is argued to be important not only in the galactic dynamo, but also in accretion discs in active galactic nuclei and around protostars, both of which contribute to producing a strong enough seed magnetic field. Although primordial magnetic fields may be too weak to compete with these astrophysical mechanisms, such fields could perhaps still be important in producing polarization effects in the cosmic background radiation. (c) 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Abstract: Aims. An efficient algorithm for calculating radiative transfer on massively parallel computers using domain decomposition is presented. Methods. The integral formulation of the transfer equation is used to divide the problem into a local but compute-intensive part for calculating the intensity and optical depth integrals, and a nonlocal part for communicating the intensity between adjacent processors. Results. The waiting time of idle processors during the nonlocal communication part does not have a severe impact on the scaling. The wall clock time thus scales nearly linearly with the inverse number of processors.
Abstract: Aims. To quantify the transient growth of nonaxisymmetric perturbations in unstratified magnetized and stratified non-magnetized rotating linear shear flows in the shearing sheet approximation of accretion disc flows. Methods. The Rayleigh quotient in modal approaches for the linearized equations (with time-dependent wavenumber) and the amplitudes from direct shearing sheet simulations using a finite difference code are compared. Results. Both approaches agree in their predicted growth behavior. The magneto-rotational instability for axisymmetric and non-axisymmetric perturbations is shown to have the same dependence of the (instantaneous) growth rate on the wavenumber along the magnetic field, but in the nonaxisymmetric case the growth is only transient. However, a meaningful dependence of the Rayleigh quotient on the radial wavenumber is obtained. While in the magnetized case the total amplification factor can be several orders of magnitude, it is only of order ten or less in the nonmagnetic case. Stratification is shown to have a stabilizing effect. In the present case of shearing-periodic boundaries the (local) strato-rotational instability seems to be absent.
Abstract: The validity of a closure called the minimal tau approximation (MTA), is tested in the context of dynamo theory, wherein triple correlations are assumed to provide relaxation of the turbulent electromotive force. Under MTA, the alpha effect in mean field dynamo theory becomes proportional to a relaxation time scale multiplied by the difference between kinetic and current helicities. It is shown that the value of the relaxation time is positive and, in units of the turnover time at the forcing wavenumber, it is of the order of unity. It is quenched by the magnetic field - roughly independently of the magnetic Reynolds number. However, this independence becomes uncertain at large magnetic Reynolds number. Kinetic and current helicities are shown to be dominated by large scale properties of the flow.
Abstract: The current understanding of astrophysical magnetic fields is reviewed, focusing on their generation and maintenance by turbulence. In the astrophysical context this generation is usually explained by a self-excited dynamo, which involves flows that can amplify a weak 'seed' magnetic field exponentially fast. Particular emphasis is placed on the nonlinear saturation of the dynamo. Analytic and numerical results are discussed both for small scale dynamos, which are completely isotropic, and for large scale dynamos, where some form of parity breaking is crucial. Central to the discussion of large scale dynamos is the so-called alpha effect which explains the generation of a mean field if the turbulence lacks mirror symmetry, i.e. if the flow has kinetic helicity. Large scale dynamos produce small scale helical fields as a waste product that quench the large scale dynamo and hence the alpha effect. With this in mind, the microscopic theory of the alpha effect is revisited in full detail and recent results for the loss of helical magnetic fields are reviewed. (c) 2005 Elsevier B.V. All rights reserved.
Abstract: Numerical simulations of turbulent stratified convection are used to study models with approximately the same convective flux, but different radiative fluxes. As the radiative flux is decreased, for constant convective flux: the entropy jump at the top of the convection zone becomes steeper, the temperature fluctuations increase and the velocity fluctuations decrease in magnitude, and the distance that low entropy fluid from the surface can penetrate increases. Velocity and temperature fluctuations follow mixing length scaling laws.
Abstract: The stability and conservation properties of a recently proposed polymerization model are studied. The achiral (racemic) solution is linearly unstable once the relevant control parameter (here the fidelity of the catalyst) exceeds a critical value. The growth rate is calculated for different fidelity parameters and cross-inhibition rates. A chirality parameter is defined and shown to be conserved by the nonlinear terms of the model. Finally, a truncated version of the model is used to derive a set of two ordinary differential equations and it is argued that these equations are more realistic than those used in earlier models of that form.
Abstract: We study the evolution of growth and decay laws for the magnetic field coherence length, energy EM and magnetic helicity H in freely decaying 3D MHD turbulence. We show that with certain assumptions, self-similarity of the magnetic power spectrum alone implies that xi similar to t(1/2). This in turn implies that magnetic helicity decays as H similar to t(-2s), where s = (xi(diff)/xi(H))(2), in terms of xi(diff), the diffusion length scale, and xi(H), a length scale defined from the helicity power spectrum. The relative magnetic helicity remains constant, implying that the magnetic energy decays as E-M similar to t(-1/2-2s). The parameter s is inversely proportional to the magnetic Reynolds number Re-M, which is constant in the self-similar regime.
Abstract: Several one and two dimensional mean field models are analyzed where the effects of current helicity fluxes and boundaries are included within the framework of the dynamical quenching model. In contrast to the case with periodic boundary conditions, the final saturation energy of the mean field decreases inversely proportional to the magnetic Reynolds number. If a nondimensional scaling factor in the current helicity flux exceeds a certain critical value, the dynamo can operate even without kinetic helicity, i.e. it is based only on shear and current helicity fluxes, as first suggested by Vishniac & Cho. Only above this threshold is the current helicity flux also able to alleviate catastrophic quenching. The fact that certain turbulence: simulations have now shown apparently non-resistively limited mean field saturation amplitudes may be suggestive of the current helicity flux having exceeded this critical value. Even below this critical value the field still reaches appreciable strength at the end of the kinematic phase, which is in qualitative agreement with dynamos in periodic domains. However, for large magnetic Reynolds numbers the field undergoes subsequent variations on a resistive time scale when, for long periods, the field can be extremely weak.
Abstract: The excitation of internal gravity waves by penetrative convective plumes is investigated using 2-D direct simulations of compressible convection. The wave generation is quantitatively studied from the linear response of the radiative zone to the plumes penetration, using projections onto the g-modes solutions of the associated linear eigenvalue problem for the perturbations. This allows an accurate determination of both the spectrum and amplitudes of the stochastically excited modes. Using time-frequency diagrams of the mode amplitudes, we then show that the lifetime of a mode is around twice its period and that during times of significant excitation up to 40% of the total kinetic energy may be contained into g- modes.
Abstract: Three closely related stumbling blocks of solar mean field dynamo theory are discussed: how dominant are the small scale fields, how is the alpha effect quenched, and whether magnetic and current helicity fluxes alleviate the quenching? It is shown that even at the largest currently available resolution there is no clear evidence of power law scaling of the magnetic and kinetic energy spectra in turbulence. However, using subgrid scale modeling, some indications of asymptotic equipartition can be found. The frequently used first order smoothing approach to calculate the alpha effect and other transport coefficients is contrasted with the superior minimal tau approximation. The possibility of catastrophic alpha quenching is discussed as a result of magnetic helicity conservation. Magnetic and current helicity fluxes are shown to alleviate catastrophic quenching in the presence of shear. Evidence for strong large scale dynamo action, even in the absence of helicity in the forcing, is presented.
Abstract: Accretion disc turbulence is investigated in the framework of the shearing box approximation. The turbulence is either driven by the magneto-rotational instability or, in the non-magnetic case, by an explicit and artificial forcing term in the momentum equation. Unlike the magnetic case, where most of the dissipation occurs in the disc corona, in the forced hydrodynamic case most of the dissipation occurs near the midplane. In the hydrodynamic case evidence is presented for the stochastic excitation of epicycles. When the vertical and radial epicyclic frequencies are different (modeling the properties around rotating black holes), the beat frequency between these two frequencies appear to show up as a peak in the temporal power spectrum in some cases. Finally, the full turbulent resistivity tensor is determined and it is found that, if the turbulence is driven by a forcing term, the signs of its off-diagonal components are such that this effect would not be capable of dynamo action by the shear-current effect.
Abstract: We study numerically the dependence of the critical magnetic Reynolds number for the turbulent small-scale scale dynamo on the hydrodynamic Reynolds number. The turbulence is statistically homogeneous, isotropic, Re and mirror-symmetric. We are interested in the regime of low magnetic Prandtl number, which Pm = Rm/Re < 1 is relevant for stellar convective zones, protostellar disks, and laboratory liquid-metal experiments. The two asymptotic possibilities are Rm(c) -> const as Re -> infinity (a small-scale dynamo exists at low) or Rm(c)/Re = Pmc -> const Re -> infinity (no small-scale dynamo exists at low). Results obtained in two independent sets of simulations of MHD turbulence using grid and spectral codes are brought together and found to be in quantitative agreement. We find that at currently accessible resolutions, grows with with no sign of approaching a Rm Re constant limit. We reach the maximum values of for. By comparing simulations with Rm(c) similar to 500 Re similar to 3000 Laplacian viscosity, fourth-, sixth-, and eighth-order hyperviscosity, and Smagorinsky large-eddy viscosity, we find that is not sensitive to the particular form of the viscous cutoff. This work represents a significant Rm c extension of the studies previously published by Schekochihin et al. (2004a) and Haugen et al. (2004a) and the first detailed scan of the numerically accessible part of the stability curve. Rm(c) (Re).
Abstract: Arguments for and against the widely accepted picture of a solar dynamo being seated in the tachocline are reviewed, and alternative ideas concerning dynamos operating in the bulk of the convection zone, or perhaps even in the near-surface shear layer, are discussed. Based on the angular velocities of magnetic tracers, it is argued that the observations are compatible with a distributed dynamo that may be strongly shaped by the near-surface shear layer. Direct simulations of dynamo action in a slab with turbulence and shear are presented to discuss filling factor and tilt angles of bipolar regions in such a model.
Abstract: The stability and conservation properties of a recently proposed polymerization model are studied. The achiral (racemic) solution is linearly unstable once the relevant control parameter (here the fidelity of the catalyst) exceeds a critical value. The growth rate is calculated for different fidelity parameters and cross-inhibition rates. A chirality parameter is defined and shown to be conserved by the nonlinear terms of the model. Finally, a truncated version of the model is used to derive a set of two ordinary differential equations and it is argued that these equations are more realistic than those used in earlier models of that form.
Abstract: It is argued that much of the observed magnetic helicity losses at the solar surface may represent a reduction of an otherwise more dominant nonlinearity of solar and stellar dynamos. This nonlinearity is proportional to the internal twist (as opposed to writhe) of helical and sigmoidal surface structures.
Abstract: It is argued that much of the observed magnetic helicity losses at the solar surface may represent a reduction of an otherwise more dominant nonlinearity of solar and stellar dynamos. This nonlinearity is proportional to the internal twist (as opposed to writhe) of helical and sigmoidal surface structures.
Abstract: Three-dimensional turbulence simulations are used to show that the turbulent root mean square velocity is an upper bound of the speed of turbulent diffusion. There is a close analogy to magnetic diffusion where the maximum diffusion speed is the speed of light. Mathematically, this is caused by the inclusion of the Faraday displacement current which ensures that causality is obeyed. In turbulent diffusion, a term similar to the displacement current emerges quite naturally when the minimal tau approximation is used. Simulations confirm the presence of such a term and give a quantitative measure of its relative importance.
Abstract: A fully self-contained model of homochirality is presented that contains the effects of both polymerization and dissociation. The dissociation fragments are assumed to replenish the substrate from which new monomers can grow and undergo new polymerization. The mean length of isotactic polymers is found to grow slowly with the normalized total number of corresponding building blocks. Alternatively, if one assumes that the dissociation fragments themselves can polymerize further, then this corresponds to a strong source of short polymers, and an unrealistically short average length of only 3. By contrast, without dissociation, isotactic polymers becomes infinitely long.
Abstract: A fully self-contained model of homochirality is presented that contains the effects of both polymerization and dissociation. The dissociation fragments are assumed to replenish the substrate from which new monomers can grow and undergo new polymerization. The mean length of isotactic polymers is found to grow slowly with the normalized total number of corresponding building blocks. Alternatively, if one assumes that the dissociation fragments themselves can polymerize further, then this corresponds to a strong source of short polymers, and an unrealistically short average length of only 3. By contrast, without dissociation, isotactic polymers becomes infinitely long.
Abstract: A fully self-contained model of homochirality is presented that contains the effects of both polymerization and dissociation. The dissociation fragments are assumed to replenish the substrate from which new monomers can grow and undergo new polymerization. The mean length of isotactic polymers is found to grow slowly with the normalized total number of corresponding building blocks. Alternatively, if one assumes that the dissociation fragments themselves can polymerize further, then this corresponds to a strong source of short polymers, and an unrealistically short average length of only 3. By contrast, without dissociation, isotactic polymers becomes infinitely long.
Abstract: The excitation of internal gravity waves by an entropy bubble oscillating in an isothermal atmosphere is investigated using direct two-dimensional numerical simulations. The oscillation field is measured by a projection of the simulated velocity field onto the anelastic solutions of the linear eigenvalue problem for the perturbations. This facilitates a quantitative study of both the spectrum and the amplitudes of excited g-modes.
Abstract: Numerical turbulence with hyperviscosity is studied and compared with direct simulations using ordinary viscosity and data from wind tunnel experiments. It is shown that the inertial range scaling is similar in all three cases. Furthermore, the bottleneck effect is approximately equally broad (about one order of magnitude) in these cases and only its height is increased in the hyperviscous case-presumably as a consequence of the steeper decent of the spectrum in the hyperviscous subrange. The mean normalized dissipation rate is found to be in agreement with both wind tunnel experiments and direct simulations. The structure function exponents agree with the She-Leveque model. Decaying turbulence with hyperviscosity still gives the usual t(-1.25) decay law for the kinetic energy, and also the bottleneck effect is still present and about equally strong.
Abstract: Nonhelical hydromagnetic forced turbulence is investigated using large scale simulations on up to 256 processors and 1024(3) mesh points. The magnetic Prandtl number is varied between 1/8 and 30, although in most cases it is unity. When the magnetic Reynolds number is based on the inverse forcing wave number, the critical value for dynamo action is shown to be around 35 for magnetic Prandtl number of unity. For small magnetic Prandtl numbers we find the critical magnetic Reynolds number to increase with decreasing magnetic Prandtl number. The Kazantsev k(3/2) spectrum for magnetic energy is confirmed for the kinematic regime, i.e., when nonlinear effects are still unimportant and when the magnetic Prandtl number is unity. In the nonlinear regime, the energy budget converges for large Reynolds numbers (around 1000) such that for our parameters about 70% is in kinetic energy and about 30% is in magnetic energy. The energy dissipation rates are converged to 30% viscous dissipation and 70% resistive dissipation. Second-order structure functions of the Elsasser variables give evidence for a k(-5/3) spectrum. Nevertheless, the three-dimensional spectrum is close to k(-3/2), but we argue that this is due to the bottleneck effect. The bottleneck effect is shown to be equally strong both for magnetic and nonmagnetic turbulence, but it is far weaker in one-dimensional spectra that are normally studied in laboratory turbulence. Structure function exponents for other orders are well described by the She-Leveque formula, but the velocity field is significantly less intermittent and the magnetic field is more intermittent than the Elsasser variables.
Abstract: The effect of compressibility on the onset of non-helical turbulent dynamo action is investigated using both direct simulations as well as simulations with shock-capturing viscosities, keeping, however, the regular magnetic diffusivity. It is found that the critical magnetic Reynolds number increases from about 35 in the subsonic regime to about 70 in the supersonic regime. Although the shock structures are sharper in the high-resolution direct simulations compared with the low-resolution shock-capturing simulations, the magnetic field looks roughly similar in both cases and does not show any shock structures. Similarly, the onset of dynamo action is not significantly affected by the shock-capturing viscosity.
Abstract: Local three-dimensional shearing box simulations of the compressible coupled dust-gas equations are used in the fluid approximation to study the evolution of different initial vortex configurations in a protoplanetary disc and their dust-trapping capabilities. The initial conditions for the gas are derived from an analytic solution to the compressible Euler equation and the continuity equation. The solution is valid if there is a vacuum outside the vortex. In the simulations the vortex is either embedded in a hot corona, or it is extended in a cylindrical fashion in the vertical direction. Both configurations are found to survive for at least one orbit and lead to accumulation of dust inside the vortex. This confirms earlier findings that dust accumulates in anticyclonic vortices, indicating that this is a viable mechanism for planetesimal formation.
Abstract: Statistical parameters of the ISM driven by thermal energy injections from supernova explosions have been obtained from 3D, nonlinear, magnetohydrodynamic, shearing-box simulations for spiral arm and interarm regions. The density scale height obtained for the interarm regions is 50% larger than for the spiral arms because of the higher gas temperature. The filling factor of the hot gas is also significantly larger between the arms and depends sensitively on magnetic field strength.
Abstract: In helical hydromagnetic turbulence with an imposed magnetic field (which is constant in space and time) the magnetic helicity of the field within a periodic domain is no longer an invariant of the ideal equations. Alternatively, there is a generalized magnetic helicity that is an invariant of the ideal equations. It is shown that this quantity is not gauge invariant and that it can therefore not be used in practice. Instead, the evolution equation of the magnetic helicity of the field describing the deviation from the imposed field is shown to be a useful tool. It is demonstrated that this tool can determine steady state quenching of the alpha-effect. A simple three-scale model is derived to describe the evolution of the magnetic helicity and to predict its sign as a function of the imposed field strength. The results of the model agree favorably with simulations.
Abstract: Nonhelical hydromagnetic turbulence with an externally imposed magnetic field is investigated using direct numerical simulations. It is shown that the imposed magnetic field lowers the spectral magnetic energy in the inertial range. This is explained by a suppression of the small scale dynamo. At large scales, however, the spectral magnetic energy increases with increasing imposed field strength for moderately strong fields, and decreases only slightly for even stronger fields. The presence of Alfven waves is explicitly confirmed by monitoring the evolution of magnetic field and velocity at one point. The frequency omega agrees with v(A)k(1), where v(A) is the Alfven speed and k(1) is the smallest wave number in the box.
Abstract: Evidence for non-Fickian diffusion of a passive scalar is presented using direct simulations of homogeneous isotropic turbulence. The results compare favorably with an explicitly time-dependent closure model based on the tau approximation. In the numerical experiments three different cases are considered: (i) zero mean concentration with finite initial concentration flux, (ii) an initial top hat profile for the concentration, and (iii) an imposed background concentration gradient. All cases agree in the resulting relaxation time in the tau approximation relating the triple correlation to the concentration flux. The first-order smoothing approximation is shown to be inapplicable. (C) 2004 American Institute of Physics.
Abstract: The interaction between a protostellar magnetosphere and a surrounding dynamo-active accretion disc is investigated using an axisymmetric mean-field model. In all models investigated, the dynamo-generated magnetic field in the disc arranges itself such that in the corona, the field threading the disc is anti-aligned with the central dipole so that no X-point forms. When the magnetospheric field is strong enough (stellar surface field strength around 2 kG or larger), accretion happens in a recurrent fashion with periods of around 15 to 30 days, which is somewhat longer than the stellar rotation period of around 10 days. In 14 the case of a stellar Surface field strength of at least a few 100 G, the star is being spun up by the magnetic torque exerted on the star. The stellar accretion rates are always reduced by the presence of a magnetosphere which tends to divert a much larger 14 fraction of the disc material into the wind. Both, a pressure-driven stellar wind and a disc wind form. In all our models with disc dynamo. the disc wind is Structured and driven by magneto-centrifugal as well as pressure forces.
Abstract: Decaying turbulence is studied numerically using as initial condition a random flow whose shell-integrated energy spectrum increases with wave number k like k(q). Alternatively, initial conditions are generated from a driven turbulence simulation by simply stopping the driving. It is known that the dependence of the decaying energy spectrum on wave number, time, and viscosity can be collapsed onto a unique scaling function that depends only on two parameters. This is confirmed using three-dimensional simulations and the dependence of the scaling function on its two arguments is determined.
Abstract: In helical hydromagnetic turbulence with an imposed magnetic field (which is constant in space and time) the magnetic helicity of the field within a periodic domain is no longer an invariant of the ideal equations. Alternatively, there is a generalized magnetic helicity that is an invariant of the ideal equations. It is shown that this quantity is not gauge invariant and that it can therefore not be used in practice. Instead, the evolution equation of the magnetic helicity of the field describing the deviation from the imposed field is shown to be a useful tool. It is demonstrated that this tool can determine steady state quenching of the alpha-effect. A simple three-scale model is derived to describe the evolution of the magnetic helicity and to predict its sign as a function of the imposed field strength. The results of the model agree favorably with simulations.
Abstract: Decaying turbulence is studied numerically using as initial condition a random flow whose shell-integrated energy spectrum increases with wave number k like k(q). Alternatively, initial conditions are generated from a driven turbulence simulation by simply stopping the driving. It is known that the dependence of the decaying energy spectrum on wave number, time, and viscosity can be collapsed onto a unique scaling function that depends only on two parameters. This is confirmed using three-dimensional simulations and the dependence of the scaling function on its two arguments is determined.
Abstract: Nonhelical hydromagnetic forced turbulence is investigated using large scale simulations on up to 256 processors and 1024(3) mesh points. The magnetic Prandtl number is varied between 1/8 and 30, although in most cases it is unity. When the magnetic Reynolds number is based on the inverse forcing wave number, the critical value for dynamo action is shown to be around 35 for magnetic Prandtl number of unity. For small magnetic Prandtl numbers we find the critical magnetic Reynolds number to increase with decreasing magnetic Prandtl number. The Kazantsev k(3/2) spectrum for magnetic energy is confirmed for the kinematic regime, i.e., when nonlinear effects are still unimportant and when the magnetic Prandtl number is unity. In the nonlinear regime, the energy budget converges for large Reynolds numbers (around 1000) such that for our parameters about 70% is in kinetic energy and about 30% is in magnetic energy. The energy dissipation rates are converged to 30% viscous dissipation and 70% resistive dissipation. Second-order structure functions of the Elsasser variables give evidence for a k(-5/3) spectrum. Nevertheless, the three-dimensional spectrum is close to k(-3/2), but we argue that this is due to the bottleneck effect. The bottleneck effect is shown to be equally strong both for magnetic and nonmagnetic turbulence, but it is far weaker in one-dimensional spectra that are normally studied in laboratory turbulence. Structure function exponents for other orders are well described by the She-Leveque formula, but the velocity field is significantly less intermittent and the magnetic field is more intermittent than the Elsasser variables.
Abstract: Numerical turbulence with hyperviscosity is studied and compared with direct simulations using ordinary viscosity and data from wind tunnel experiments. It is shown that the inertial range scaling is similar in all three cases. Furthermore, the bottleneck effect is approximately equally broad (about one order of magnitude) in these cases and only its height is increased in the hyperviscous case-presumably as a consequence of the steeper decent of the spectrum in the hyperviscous subrange. The mean normalized dissipation rate is found to be in agreement with both wind tunnel experiments and direct simulations. The structure function exponents agree with the She-Leveque model. Decaying turbulence with hyperviscosity still gives the usual t(-1.25) decay law for the kinetic energy, and also the bottleneck effect is still present and about equally strong.
Abstract: The dimensionless kinetic energy dissipation rate C(epsilon) is estimated from numerical simulations of statistically stationary isotropic box turbulence that is slightly compressible. The Taylor microscale Reynolds number (Re(lambda)) range is 20< or approximately equal to Re(lambda) < or approximately equal to 220 and the statistical stationarity is achieved with a random phase forcing method. The strong Re(lambda) dependence of C(epsilon) abates when Re(lambda) approximately 100 after which C(epsilon) slowly approaches approximately 0.5, a value slightly different from previously reported simulations but in good agreement with experimental results. If C(epsilon) is estimated at a specific time step from the time series of the quantities involved it is necessary to account for the time lag between energy injection and energy dissipation. Also, the resulting value can differ from the ensemble averaged value by up to +/-30%. This may explain the spread in results from previously published estimates of C(epsilon).
Abstract: Nonhelical hydromagnetic turbulence with an externally imposed magnetic field is investigated using direct numerical simulations. It is shown that the imposed magnetic field lowers the spectral magnetic energy in the inertial range. This is explained by a suppression of the small scale dynamo. At large scales, however, the spectral magnetic energy increases with increasing imposed field strength for moderately strong fields, and decreases only slightly for even stronger fields. The presence of Alfve n waves is explicitly confirmed by monitoring the evolution of magnetic field and velocity at one point. The frequency omega agrees with v(A) k(1) , where v(A) is the Alfve n speed and k(1) is the smallest wave number in the box.
Abstract: Large scale dynamos produce small scale current helicity as a waste product that quenches the large scale dynamo process (alpha effect). This quenching can be catastrophic (i.e., intensify with magnetic Reynolds number) unless one has fluxes of small scale magnetic (or current) helicity out of the system. We derive the form of helicity fluxes in turbulent dynamos, taking also into account the nonlinear effects of Lorentz forces due to fluctuating fields. We confirm the form of an earlier derived magnetic helicity flux term, and also show that it is not renormalized by the small scale magnetic field, just like turbulent diffusion. Additional nonlinear fluxes are identified, which are driven by the anisotropic and antisymmetric parts of the magnetic correlations. These could provide further ways for turbulent dynamos to transport out small scale magnetic helicity, so as to avoid catastrophic quenching.
Abstract: An axisymmetric model of a cool, dynamo-active accretion disc is applied to protostellar discs. Thermally and magnetically driven outflows develop that are not collimated within 0.1 AU. In the presence of a central magnetic field from the protostar, accretion onto the protostar is highly episodic, which is in agreement with earlier work.
Abstract: Large scale dynamos produce small scale current helicity as a waste product that quenches the large scale dynamo process (alpha effect). This quenching can be catastrophic (i.e., intensify with magnetic Reynolds number) unless one has fluxes of small scale magnetic (or current) helicity out of the system. We derive the form of helicity fluxes in turbulent dynamos, taking also into account the nonlinear effects of Lorentz forces due to fluctuating fields. We confirm the form of an earlier derived magnetic helicity flux term, and also show that it is not renormalized by the small scale magnetic field, just like turbulent diffusion. Additional nonlinear fluxes are identified, which are driven by the anisotropic and antisymmetric parts of the magnetic correlations. These could provide further ways for turbulent dynamos to transport out small scale magnetic helicity, so as to avoid catastrophic quenching.
Abstract: A new simulation set-up is proposed for studying mean field dynamo action. The model combines the computational advantages of local Cartesian geometry with the ability to include a shear profile that resembles the sun's differential rotation at low latitudes. It is shown that in a two-dimensional mean field model this geometry produces cyclic solutions with dynamo waves traveling away from the equator - as expected for a positive alpha effect in the northern hemisphere. In three dimensions with turbulence driven by a helical forcing function, an alpha effect is self-consistently generated in the presence of a finite imposed toroidal magnetic field. The results suggest that, due to a finite flux of current helicity out of the domain, alpha quenching appears to be non-catastrophic - at least for intermediate values of the magnetic Reynolds number. For larger values of the magnetic Reynolds number, however, there is evidence for a reversal of the trend and that a may decrease with increasing magnetic Reynolds number. Control experiments with closed boundaries confirm that in the absence of a current helicity flux, but with shear as before, alpha quenching is always catastrophic and alpha decreases inversely proportional to the magnetic Reynolds number. For solar parameters, our results suggest a current helicity flux of about 0.001 G(2)/s. This corresponds to a magnetic helicity flux, integrated over the northern hemisphere and over the 11 year solar cycle, of about 10(46) Mx(2).
Abstract: According to the kinematic theory of nonhelical dynamo action, the magnetic energy spectrum increases with wavenumber and peaks at the resistive cutoff wavenumber. It has previously been argued that even in the dynamical case, the magnetic energy peaks at the resistive scale. Using high resolution simulations ( up to 1024(3) meshpoints) with no large-scale imposed field, we show that the magnetic energy peaks at a wavenumber that is independent of the magnetic Reynolds number and about five times larger than the forcing wavenumber. Throughout the inertial range, the spectral magnetic energy exceeds the kinetic energy by a factor of two to three. Both spectra are approximately parallel. The total energy spectrum seems to be close to k(-3/2), but there is a strong bottleneck effect and we suggest that the asymptotic spectrum is instead k(-5/3). This is supported by the value of the second-order structure function exponent that is found to be zeta(2) = 0.70, suggesting a k(-1.70) spectrum. The third-order structure function scaling exponent is very close to unity, - in agreement with Goldreich - Sridhar theory. Adding an imposed field tends to suppress the small-scale magnetic field. We find that at large scales the magnetic energy spectrum then follows a k(-1) slope. When the strength of the imposed field is of the same order as the dynamo generated field, we find almost equipartition between the magnetic and kinetic energy spectra.
Abstract: The dimensionless kinetic energy dissipation rate C-epsilon is estimated from numerical Simulations of statistically stationary isotropic box turbulence that is slightly compressible. The Taylor microscale Reynolds number (Re-lambda) range is 20 less than or similar to Re-lambda less than or similar to220 and the statistical stationarity is achieved with a random phase forcing method. The strong Re-lambda dependence of C-epsilon abates when Re-lambda approximate to 100 after which C-epsilon slowly approaches approximate to0.5. a value Slightly different from previously reported simulations but in good agreement with experimental results. If C-epsilon is estimated at a specific time step from the time series of the quantities involved it is necessary to account for the time lag between energy injection and energy dissipation. Also. the resulting value can differ from the ensemble averaged value by up to +/-30%. This may explain the spread in results from previously published estimates of C-epsilon.
Abstract: Numerical simulations of the multi-phase interstellar medium have been carried out, using a 3D, nonlinear, magnetohydrodynamic, shearing-box model, with random motions driven by supernova explosions. These calculations incorporate the effects of magnetic fields and rotation in 3D; these play important dynamical roles in the galaxy, but are neglected in many other simulations. The supernovae driving the motions are not arbitrarily imposed, but occur where gas accumulates into cold, dense clouds; their implementation uses a physically motivated model for the evolution of such clouds. The process is self-regulating, and produces mean supernova rates as part of the solution. Simulations with differing mean density show a power law relation between the supernova rate and density, with exponent 1.7; this value is within the range suggested from observations ( taking star formation rate as a proxy for supernova rate). The global structure of the supernova driven medium is strongly affected by the presence of magnetic fields; e.g. for one solution the filling factor of hot gas is found to vary from 0.19 ( with no field) to 0.12 (with initial mid-plane field B-0 = 6 muG).
Abstract: Two different computational approaches to the magnetorotational instability (MRI) are pursued: the shearing box approach which is suited for local simulations and the embedding box approach whereby a Taylor Couette flow is embedded in a box so that numerical problems with the coordinate singularity are avoided. New shearing box simulations are presented and differences between regular and hyperviscosity are discussed. Preliminary Simulations of spherical nonlinear Taylor Couette flow in an embedding box are presented and the effects of an axial field on the background flow are Studied.
Abstract: The principle of the two-scale dynamo experiment at the Forschungszentrum Karlsruhe is closely related to that of the Roberts dynamo working with a simple fluid flow which is, with respect to proper Cartesian coordinates x, y, and z, periodic in x and y and independent of z. A modified Roberts dynamo problem is considered with a flow more similar to that in the experimental device. Solutions are calculated numerically, and on this basis an estimate of the excitation condition of the experimental dynamo is given. The modified Roberts dynamo problem is also considered in the framework of the mean-field dynamo theory, in which the crucial induction effect of the fluid motion is an anisotropic alpha effect. Numerical results are given for the dependence of the mean-field coefficients on the fluid flow rates. The excitation condition of the dynamo is also discussed within this framework. The behavior of the dynamo in the nonlinear regime, i.e., with backreaction of the magnetic field on the fluid flow, depends on the effect of the Lorentz force on the flow rates. The quantities determining this effect are calculated numerically. The results for the mean-field coefficients and the quantities describing the backreaction provide corrections to earlier results, which were obtained under simplifying assumptions.
Abstract: At numerical resolutions around 512(3) and above, three-dimensional energy spectra from turbulence simulations begin to show noticeably shallower spectra than k(-5/3) near the dissipation wave number ("bottleneck effect"). This effect is shown to be significantly weaker in one-dimensional spectra such as those obtained in wind tunnel turbulence. The difference can be understood in terms of the transformation between the one-dimensional and three-dimensional energy spectra under the assumption that the turbulent velocity field is isotropic. Transversal and longitudinal energy spectra are similar and can both accurately be computed from the full three-dimensional spectra. Second-order structure functions are less susceptible to the bottleneck effect and may be better suited for inferring the scaling exponent from numerical simulation data.
Abstract: Isotropic homogeneous hydromagnetic turbulence is studied using numerical simulations at resolutions of up to 1024(3) meshpoints. It is argued that, in contrast to the kinematic regime, the nonlinear regime is characterized by a spectral magnetic power that is decreasing with increasing wavenumber, regardless of whether or not the turbulence has helicity. This means that the root-mean-square field strength converges to a limiting value at large magnetic Reynolds numbers. The total (magnetic and kinetic) energy spectrum tends to be somewhat shallower than k(-5/3), in agreement with the findings of other groups. In the presence of helicity, an inverse cascade develops, provided the scale separation between the size of the computational box and the scale of the energy carrying eddies exceeds a ratio of at least two. Finally, the constraints imposed by magnetic helicity conservation on mean-field theory are reviewed and new results of simulations are presented.
Abstract: Over the past few years there has been growing interest in helical magnetic field structures seen at the solar surface, in coronal mass ejections, as well as in the solar wind. Although there is a great deal of randomness in the data, on average the extended structures are mostly left-handed on the northern hemisphere and right-handed on the southern. Surface field structures are also classified as dextral (= right bearing) and sinistral (= left bearing) occurring preferentially in the northern and southern hemispheres respectively. Of particular interest here is a quantitative measurement of the associated emergence rates of helical structures, which translate to magnetic helicity fluxes. In this review, we give a brief survey of what has been found so far and what is expected based on models. Particular emphasis is put on the scale dependence of the associated fields and an attempt is made to estimate the helicity flux of the mean field vs. fluctuating field.
Abstract: We present an axisymmetric numerical model of a dynamo active accretion disc. If the dynamo-generated magnetic field in the disc is sufficiently strong (close to equipartition with thermal energy), a fast magneto-centrifugally driven outflow develops within a conical shell near the rotation axis, together with a slower pressure driven outflow from the outer parts of the disc as well as around the axis. Our results show that a dynamo active accretion disc can contribute to driving an outflow even without any external magnetic field. The fast outflow in the conical shell is confined by the azimuthal field which is produced by the dynamo in the disc and advected to the disc corona. This part of the outflow has high angular momentum and is cooler and less dense than its surroundings. The conical shell's half-opening angle is typically about 30 near the disc and decreases slightly with height. The slow outflow is hotter and denser.
Abstract: Two questions about the solar magnetic field might be answered together once their connection is identified. The first is important for large-scale dynamo theory: what prevents the magnetic back- reaction forces from shutting down the dynamo cycle? The second question is, what determines the handedness of twist and writhe in magnetized coronal ejecta? Magnetic helicity conservation is important for answering both questions. Conservation implies that dynamo generation of large-scale writhed structures is accompanied by the oppositely signed twist along these structures. The latter is associated with the back- reaction force. We suggest that coronal mass ejections simultaneously liberate small-scale twist and large-scale writhe of opposite sign, helping to prevent the cycle from quenching and enabling a net magnetic flux change in each hemisphere. Solar observations and helicity spectrum measurements from our simulation of a rising flux tube support this idea. We show a new pictorial of dynamo flux generation that includes the back- reaction and magnetic helicity conservation and represents the field by a ribbon or tube rather than a line.
Abstract: 'The connection between helically isotropic MHD turbulence and mean-field dynamo theory is reviewed. The nonlinearity in the mean-field theory is not yet well established, but detailed comparison with simulations begin to help select viable forms of the nonlinearity. The crucial discriminant is the magnetic helicity; which is known to evolve only on a slow resistive time scale in the limit of large magnetic Reynolds number. Particular emphasis is put on the possibility of memory effects, which means that an additional explicitly time-dependent equation for the nonlinearity is solved simultaneously with the mean-field equations. This approach leads to better agreement with the simulations, while it would also produce more favorable agreement between models and stellar dynamos.
Abstract: There is mounting evidence that the ejection of magnetic helicity from the solar surface is important for the solar dynamo. Observations suggest that in the northern hemisphere the magnetic helicity flux is negative. We propose that this magnetic helicity flux is mostly due to small scale magnetic fields; in contrast to the more systematic large scale field of the 11 year cycle, whose helicity flux may be of opposite sign, and may be excluded from the observational interpretation. Using idealized simulations of MHD turbulence as well as a simple two-scale model, we show that shedding small scale (helical) field has two important effects. (i) The strength of the large scale field reaches the observed levels. (ii) The evolution of the large scale field proceeds on time scales shorter than the resistive time scale, as would otherwise be enforced by magnetic helicity conservation. In other words, the losses ensure that the solar dynamo is always in the near-kinematic regime. This requires, however, that the ratio of small scale to large scale losses cannot be too small, for otherwise the large scale field in the near-kinematic regime will not-reach the observed values. (C) 2003 COSPAR. Published by Elsevier Ltd. All rights reserved.
Abstract: Over the past few years there has been growing interest in helical magnetic field structures seen at the solar surface, in coronal mass ejections, as well as in the solar wind. Although there is a great deal of randomness in the data, on average the extended structures are mostly left-handed on the northern hemisphere and right-handed on the southern. Surface field structures are also classified as dextral (= right bearing) and sinistral (= left bearing) occurring preferentially in the northern and southern hemispheres respectively. Of particular interest here is a quantitative measurement of the associated emergence rates of helical structures, which translate to magnetic helicity fluxes. In this review, we give a brief survey of what has been found so far and what is expected based on models. Particular emphasis is put on the scale dependence of the associated fields and an attempt is made to estimate the helicity flux of the mean field vs. fluctuating field.
Abstract: Nonhelical hydromagnetic turbulence without an imposed magnetic field is considered in the case where the magnetic Prandtl number is unity. The magnetic field is entirely due to dynamo action. The magnetic energy spectrum peaks at a wavenumber of about 5 times the minimum wavenumber in the domain, and not at the resistive scale, as has previously been argued. Throughout the inertial range, the spectral magnetic energy exceeds the kinetic energy by a factor of about 2.5, and both spectra are approximately parallel. At first glance, the total energy spectrum seems to be close to k(-3/2), but there is a strong bottleneck effect and it is suggested that the asymptotic spectrum is k(-5/3). This is supported by the value of the second-order structure function exponent that is found to be zeta(2)=0.70, suggesting a k(-1.70) spectrum.
Abstract: Forced turbulence simulations are used to determine the turbulent kinematic viscosity, v(t), from the decay rate of a large scale velocity field. Likewise, the turbulent magnetic diffusivity, eta(t), is determined from the decay of a large scale magnetic field. In the kinematic regime, when the field is weak, the turbulent magnetic Prandtl number, v(t)/eta(t), is about unity. When the field is nonhelical, eta(t) is quenched when magnetic and kinetic energies become comparable. For helical fields the quenching is stronger and can be described by a dynamical quenching formula.
Abstract: At numerical resolutions around 512(3) and above, three-dimensional energy spectra from turbulence simulations begin to show noticeably shallower spectra than k(-5/3) near the dissipation wave number ("bottleneck effect"). This effect is shown to be significantly weaker in one-dimensional spectra such as those obtained in wind tunnel turbulence. The difference can be understood in terms of the transformation between the one-dimensional and three-dimensional energy spectra under the assumption that the turbulent velocity field is isotropic. Transversal and longitudinal energy spectra are similar and can both accurately be computed from the full three-dimensional spectra. Second-order structure functions are less susceptible to the bottleneck effect and may be better suited for inferring the scaling exponent from numerical simulation data.
Abstract: The excitation of gravity waves by penetrative convective plumes is investigated using 2D direct simulations of compressible convection. The oscillation field is measured by a new technique based on the projection of our simulation data onto the theoretical g-modes solutions of the associated linear eigenvalue problem. This allows us to determine both the excited modes and their corresponding amplitudes accurately.
Abstract: The principle of the two-scale dynamo experiment at the Forschungszentrum Karlsruhe is closely related to that of the Roberts dynamo working with a simple fluid flow which is, with respect to proper Cartesian coordinates x, y, and z, periodic in x and y and independent of z. A modified Roberts dynamo problem is considered with a flow more similar to that in the experimental device. Solutions are calculated numerically, and on this basis an estimate of the excitation condition of the experimental dynamo is given. The modified Roberts dynamo problem is also considered in the framework of the mean-field dynamo theory, in which the crucial induction effect of the fluid motion is an anisotropic alpha effect. Numerical results are given for the dependence of the mean-field coefficients on the fluid flow rates. The excitation condition of the dynamo is also discussed within this framework. The behavior of the dynamo in the nonlinear regime, i.e., with backreaction of the magnetic field on the fluid flow, depends on the effect of the Lorentz force on the flow rates. The quantities determining this effect are calculated numerically. The results for the mean-field coefficients and the quantities describing the backreaction provide corrections to earlier results, which were obtained under simplifying assumptions.
Abstract: In the past few years suggestions have emerged that the solar magnetic field might have a bi-helical contribution with oppositely polarized magnetic fields at large and small scales, and that the shedding of such fields may be crucial for the operation of the dynamo. It is shown that, if a bi-helical field is shed into the solar wind, positive and negative contributions of the magnetic helicity spectrum tend to mix and decay. Even in the absence of turbulence, mixing and decay can occur on a time scale faster than the resistive one provided the two signs of magnetic helicity originate from a single tube. In the presence of turbulence, positively and negatively polarized contributions mix rapidly in such a way that the ratio of magnetic helicity to magnetic energy is largest both at the largest scale and in the dissipation range. In absolute units the small scale excess of helical fields is however negligible.
Abstract: The self-excitation of magnetic field by a spiral Couette flow between two coaxial cylinders is considered. We solve numerically the fully nonlinear, three-dimensional magnetohydrodynamic (MHD) equations for magnetic Prandtl numbers P(m) (ratio of kinematic viscosity to magnetic diffusivity) between 0.14 and 10 and kinematic and magnetic Reynolds numbers up to about 2000. In the initial stage of exponential field growth (kinematic dynamo regime), we find that the dynamo switches from one distinct regime to another as the radial width delta(r)(B) of the magnetic field distribution becomes smaller than the separation of the field maximum from the flow boundary. The saturation of magnetic field growth is due to a reduction in the velocity shear resulting mainly from the azimuthally and axially averaged part of the Lorentz force, which agrees with an asymptotic result for the limit of P(m)<<1. In the parameter regime considered, the magnetic energy decreases with kinematic Reynolds number as Re-0.84, which is approximately as predicted by the nonlinear asymptotic theory (approximately Re(-1)). However, when the velocity field is maintained by a volume force (rather than by viscous stress) the dependence of magnetic energy on the kinematic Reynolds number is much weaker.
Abstract: The self-excitation of magnetic field by a spiral Couette flow between two coaxial cylinders is considered. We solve numerically the fully nonlinear, three-dimensional magnetohydrodynamic (MHD) equations for magnetic Prandtl numbers P-m (ratio of kinematic viscosity to magnetic diffusivity! between 0.14 and 10 and kinematic and magnetic Reynolds numbers up to about 2000. In the initial stage of exponential field growth (kinematic dynamo regime), we find that the dynamo switches from one distinct regime to another as the radial width deltar(B) of the magnetic field distribution becomes smaller than the separation of the field maximum from the flow boundary. The saturation of magnetic field growth is due to a reduction in the velocity shear resulting mainly from the azimuthally and axially averaged part of the Lorentz force, which agrees with an asymptotic result for the limit of P-m<<1. In the parameter regime considered, the magnetic energy decreases with kinematic Reynolds number as Re-0.84, which is approximately as predicted by the nonlinear asymptotic theory (similar toRe(-1)). However, when the velocity field is maintained by a volume force (rather than by viscous stress! the dependence of magnetic energy on the kinematic Reynolds number is much weaker.
Abstract: We investigate numerically the coupled diffusion-advective type field equations originating from the canonical phase space approach to the noisy Burgers equation or the equivalent Kardar-Parisi-Zhang equation in one spatial dimension. The equations support stable right hand and left hand solitons and in the low viscosity limit a long-lived soliton pair excitation. We find that two identical pair excitations scatter transparently subject to a size-dependent phase shift and that identical solitons scatter on a static soliton transparently without a phase shift. The soliton pair excitation and the scattering configurations are interpreted in terms of growing step and nucleation events in the interface growth profile. Finally, we show that growing steps perform an anomalous random walk with dynamic exponent z=3/2.
Abstract: In numerical studies of turbulence, hyperviscosity is often used as a tool to extend the inertial subrange and to reduce the dissipative subrange. By analogy, hyperdiffusivity (or hyperresistivity) is sometimes used in magnetohydrodynamics. The underlying assumption is that only the small scales are affected by this manipulation. In the present paper, possible side effects on the evolution of the large-scale magnetic field are investigated. It is found that for turbulent flows with helicity, hyperdiffusivity causes the dynamo-generated magnetic field to saturate at a higher level than normal diffusivity. This result is successfully interpreted in terms of magnetic helicity conservation, which also predicts that full saturation is reached only after a time comparable to the large-scale magnetic (hyper)diffusion time.
Abstract: In numerical studies of turbulence, hyperviscosity is often used as a tool to extend the inertial subrange and to reduce the dissipative subrange. By analogy, hyperdiffusivity (or hyperresistivity) is sometimes used in magnetohydrodynamics. The underlying assumption is that only the small scales are affected by this manipulation. In the present paper, possible side effects on the evolution of the large-scale magnetic field are investigated. It is found that for turbulent flows with helicity, hyperdiffusivity causes the dynamo-generated magnetic field to saturate at a higher level than normal diffusivity. This result is successfully interpreted in terms of magnetic helicity conservation, which also predicts that full saturation is reached only after a time comparable to the large-scale magnetic (hyper)diffusion time.
Abstract: Using a periodic box calculation it is shown that, owing to helicity conservation, a large scale field can only develop on a resistive timescale. This behaviour can be reproduced by a mean-field dynamo with alpha and eta(t) quenchings that are equally strong and 'catastrophic'.
Abstract: We supplement the mean field dynamo growth equation with the total magnetic helicity evolution equation. This provides an explicitly time-dependent model for alpha-quenching in dynamo theory. For dynamos without shear, this approach accounts for the observed large-scale field growth and saturation in numerical simulations. After a significant kinematic phase, the dynamo is resistively quenched, i.e., the saturation time depends on the microscopic resistivity. This is independent of whether or not the turbulent diffusivity is resistively quenched. We find that the approach is also successful for dynamos that include shear and exhibit migratory waves ( cycles). In this case, however, whether or not the cycle period remains of the order of the dynamical timescale at large magnetic Reynolds numbers does depend on how the turbulent magnetic diffusivity quenches. Since this is unconstrained by magnetic helicity conservation, the diffusivity is currently an input parameter. Comparison with current numerical experiments suggests a turbulent diffusivity that depends only weakly on the magnetic Reynolds number, but higher resolution simulations are needed.
Abstract: Various approaches to estimate turbulent transport coefficients from numerical simulations of hydromagnetic turbulence are discussed. A quantitative comparison between the averaged magnetic field obtained from a specific three-dimensional simulation of a rotating turbulent shear flow in a slab and a simple one-dimensional alpha omega dynamo model is given. A direct determination of transport coefficients is attempted by calculating the correlation matrix of different components of the field and its derivatives. This matrix relates the electromotive force to physically relevant parameters like the tensor components of the alpha-effect and the turbulent diffusivity. The alpha-effect operating on the toroidal field is found to be negative and of similar magnitude as the value obtained in previous work by correlating the electromotive force with the mean magnetic field. The turbulent diffusion of the toroidal field is comparable to the kinematic viscosity that was determined earlier by comparing the stress with the shear. However, the turbulent diffusion of the radial field component is smaller and can even be formally negative. The method is then modified to obtain the spectral dependence of the turbulent transport coefficients on the wavenumber. There is evidence for nonlocal behaviour in that most of the response comes from the smallest wavenumbers corresponding to the largest scale possible in the simulation. Again, the turbulent diffusion coefficient for the radial field component is small, or even negative, which is considered unphysical. However, when the diffusion tensor is assumed to be diagonal the radial component of the diffusion tensor is positive, supporting thus the relevance of a nonlocal approach. Finally, model calculations are presented using nonlocal prescriptions of the alpha-effect and the turbulent diffusion. We emphasize that in all cases the electromotive force exhibits a strong stochastic component which make the alpha-effect and the turbulent diffusion intrinsically noisy.
Abstract: Over the past few years there has been growing interest in helical magnetic field structures seen at the solar surface, in coronal mass ejections, as well as in the solar wind. Although there is a great deal of randomness in the data, on average the extended structures are mostly left-handed on the northern hemisphere and right-handed on the southern. Surface field structures are also classified as dextral (= right bearing) and sinistral (= left bearing) occurring preferentially in the northern and southern hemispheres respectively. Of particular interest here is a quantitative measurement of the associated emergence rates of helical structures, which translate to magnetic helicity fluxes. In this review, we give a brief survey of what has been found so far and what is expected based on models. Particular emphasis is put on the scale dependence of the associated fields and an attempt is made to estimate the helicity flux of the mean field vs. fluctuating field.
Abstract: The theory of large scale dynamos is reviewed with particular emphasis on the magnetic helicity constraint in the presence of closed and open boundaries. In the presence of closed or periodic boundaries, helical dynamos respond to the helicity constraint by developing small scale separation in the kinematic regime, and by showing long time scales in the nonlinear regime where the scale separation has grown to the maximum possible value. A resistively limited evolution towards saturation is also found at intermediate scales before the largest scale of the system is reached. Larger aspect ratios can give rise to different structures of the mean field which are obtained at early times, but the final saturation field strength is still decreasing with decreasing resistivity. In the presence of shear. cyclic magnetic fields are found whose period is increasing with decreasing resistivity, but the saturation energy of the mean field is in strong super-equipartition with the turbulent energy. It is shown that artificially induced losses of small scale field of opposite sign of magnetic helicity as the large scale field can, at least in principle. accelerate the production of large scale (poloidal) field. Based on mean field models with an outer potential field boundary condition in spherical geometry. we verify that the sign of the magnetic helicity flux from the large scale field agrees with the sign of alpha. For solar parameters. typical magnetic helicity fluxes lie around 10(47) Mx(2) per cycle.
Abstract: We study the pumping of magnetic flux in three-dimensional compressible magnetoconvection in the context of stellar dynamos. The simulation domain represents a rectangular section from the lower part of a stellar convection zone plus the underlying stably stratified layer, with a total depth of up to five pressure scale heights. Once convection has attained a statistically stationary state, a magnetic field is introduced. The magnetic field is subsequently modified by the convective motions, and the resulting pumping effects are isolated by calculating various coefficients of the expansion of the electromotive force, (u x b) over bar, in terms of components of the mean magnetic field. The dependence of the pumping effects on rotation, latitude and other parameters is studied. First numerical evidence is found for the existence of pumping effects in the horizontal directions. Evidence is found that the pumping effects act differently on different components of the mean magnetic field. Latitudinal pumping is mainly equatorward for a toroidal field, and can be poleward for a poloidal field. Longitudinal pumping is mainly retrograde for the radial field but prograde for the latitudinal field. The pumping effect in the vertical direction is found to be dominated by the diamagnetic effect, equivalent to a predominating downward advection with a maximum speed in the turbulent case of about 10% of the rms convective velocity. Where possible, an attempt is made to identify the physical origin of the effect. Finally, some consequences of the results for stellar dynamos are discussed.
Abstract: We investigate numerically the coupled diffusion-advective type field equations originating from the canonical phase space approach to the noisy Burgers equation or the equivalent Kardar-Parisi-Zhang equation in one spatial dimension. The equations support stable right hand and left hand solitons and in the low viscosity limit a long-lived soliton pair excitation. We find that two identical pair excitations scatter transparently subject to a size-dependent phase shift and that identical solitons scatter on a static soliton transparently without a phase shift. The soliton pair excitation and the scattering configurations are interpreted in terms of growing step and nucleation events in the interface growth profile. Finally, we show that growing steps perform an anomalous random walk with dynamic exponent z=3/2.
Abstract: The usefulness of high-order schemes in astrophysical MHD turbulence simulations is discussed. Simple advection tests of hat profiles are used to compare schemes of different order. Higher order schemes generally need less explicit diffusion. In the case of a standing Burgers shock it is shown that the overall accuracy improves as the order of the scheme is increased. A memory efficient 3-step 2N-RK scheme is used. For cache efficiency, the entire set of equations is solved along pencils in the yz-plane. The advantage of solving for the magnetic vector potential is highlighted. Finally, results from a simulation of helical turbulence exhibiting large scale dynamo action are discussed. (C) 2002 Elsevier Science B.V. All rights reserved.
Abstract: Recent progress in the theory of solar and stellar dynamos is reviewed. Particular emphasis is placed on the mean-field theory which tries to describe the collective behavior of the magnetic field. In order to understand solar and stellar activity, a quantitatively reliable theory is necessary. Much of the new developments center around magnetic helicity conservation which is seen to be important in numerical simulations. Only a dynamical, explicitly time dependent theory of alpha-quenching is able to describe this behavior correctly.
Abstract: We explore the dependence of the amplitude of stellar dynamo cycle variability (as seen in the Mount Wilson Ca II HK timeseries data) on other stellar parameters. We find that the fractional cycle amplitude A(cyc) (i.e. the ratio of the peak-to-peak variation to the average) decreases somewhat with mean activity, increases with decreasing effective temperature, but is not correlated with inverse Rossby number Ro(-1). We find that A(cyc) increases with the ratio of cycle and rotational frequencies omega(cyc)/Omega along two, nearly parallel branches.
Abstract: We perform direct numerical simulations of three-dimensional freely decaying magnetohydrodynamic turbulence. For helical magnetic fields, an inverse cascade effect is observed in which power is transferred from smaller scales to larger scales. The magnetic field reaches a scaling regime with self-similar evolution, and power-law behavior at high wave numbers. We also find power-law decay in the magnetic and kinematic energies, and power-law growth in the characteristic length scale of the magnetic field.
Abstract: The dynamical friction experienced by a body moving in a gaseous medium is different from the friction in the case of a collisionless stellar system. Here we consider the orbital evolution of a gravitational perturber inside a gaseous sphere using three-dimensional simulations, ignoring however self-gravity. The results are analysed in terms of a 'local' formula with the associated Coulomb logarithm taken as a free parameter. For forced circular orbits, the asymptotic value of the component of the drag force in the direction of the velocity is a slowly varying function of the Mach number in the range 1.0-1.6. The dynamical friction time-scale for free decay orbits is typically only half as long as in the case of a collisionless background, which is in agreement with E. C. Ostriker's recent analytic result. The orbital decay rate is rather insensitive to the past history of the perturber. It is shown that, similarly to the case of stellar systems, orbits are not subject to any significant circularization. However, the dynamical friction time-scales are found to increase with increasing orbital eccentricity for the Plummer model, whilst no strong dependence on the initial eccentricity is found for the isothermal sphere.
Abstract: We perform direct numerical simulations of three-dimensional freely decaying magnetohydrodynamic turbulence. For helical magnetic fields, an inverse cascade effect is observed in which power is transfered from smaller scales to larger scales. The magnetic field reaches a scaling regime with self-similar evolution, and power-law behavior at high wave numbers. We also find power-law decay in the magnetic and kinematic energies, and power-law growth in the characteristic length scale of the magnetic field.
Abstract: A numerical model of isotropic homogeneous turbulence with helical forcing is investigated. The resulting flow, which is essentially the prototype of the alpha (2) dynamo of mean field dynamo theory, produces strong dynamo action with an additional large-scale field on the scale of the box (at wavenumber k = 1; forcing is at k = 5). This large-scale field is nearly force free and exceeds the equipartition value. As the magnetic Reynolds number R-m increases, the saturation field strength and the growth rate of the Rm dynamo increase. However, the time it takes to build up the large-scale field from equipartition to its final superequipartition value increases with magnetic Reynolds number. The large-scale field generation can be identified as being due to nonlocal interactions originating from the forcing scale, which is characteristic of the alpha -effect. Both alpha and turbulent magnetic diffusivity eta (t) are determined simultaneously using numerical experiments where the mean field is modified artificially. Both quantities are quenched in an R-m-dependent fashion. The evolution of the energy of the mean field matches that predicted by an alpha (2) dynamo model with similar alpha and eta (t) quenchings. For this model an analytic solution is given that matches the results of the simulations. The simulations are numerically robust in that the shape of the spectrum at large scales is unchanged when changing the resolution from 30(3) to 120(3) mesh points, or when increasing the magnetic Prandtl number (viscosity/magnetic diffusivity) from 1 to 100. Increasing the forcing wavenumber to 30 (i.e., increasing the scale separation) makes the inverse cascade effect more pronounced, although it remains otherwise qualitatively unchanged.
Abstract: The generation of large scale flows by the anisotropic kinetic alpha (AKA) effect is investigated in simulations with a suitable time-dependent space- and time-periodic anisotropic forcing lacking parity invariance. The forcing pattern moves relative to the fluid, which leads to a breaking of the Galilean invariance as required for the AKA effect to exist. The AKA effect is found to produce a clear large scale ow pattern when the Reynolds number, R, is small as only a few modes are excited in linear theory. In this case the non-vanishing components of the AKA tensor are dynamically independent of the Reynolds number. For larger values of R, many more modes are excited and the components of the AKA tensor are found to decrease rapidly with increasing value of R. However, once there is a magnetic field (imposed and of sufficient strength, or dynamo-generated and saturated) the field begins to suppress the AKA effect, regardless of the value of R. It is argued that the AKA effect is unlikely to be astrophysically significant unless the magnetic field is weak and R is small.
Abstract: A number of problems of solar and stellar dynamo theory are briefly reviewed and the current status of possible solutions is discussed. Results of direct numerical simulations are described in view of mean-field dynamo theory and the relation between the alpha-effect and the inverse cascade of magnetic helicity is highlighted. The possibility of 'catastrophic' quenching of the alpha-effect is explained in terms of the constraint placed by the conservation of magnetic helicity.
Abstract: Helicity, a measure of the linkage of flux lines, has subtle and largely unknown effects upon dynamics. Both magnetic and hydrodynamic helicity are conserved for ideal systems and could suppress nonlinear dynamics. What actually happens is not clear because in a fully three-dimensional system there are additional channels whereby intense, small-scale dynamics can occur. This contribution shows one magnetic and one hydrodynamic case where for each the presence of helicity does not suppress small-scale intense dynamics of the type that might lead to reconnection.
Abstract: The origin of large scale magnetic fields in accretion discs is investigated. Using global three-dimensional simulations of accretion disc turbulence, a recent suggestion of Vishniac & Cho (2001, ApJ 550, 752) is re-examined, according to which large scale fields in accretion discs could be understood without explicitly invoking the usual helicity effect. Particular emphasis is placed on a certain correlation between vorticity and azimuthal velocity gradient which has been predicted to drive large scale dynamo action, independent of the presence or absence of kinetic helicity. In the global disc simulations two types of behaviours are found: those which do show this type of velocity correlation and those which do not. The former ones are typically also the cases where the resistivity is larger. The latter ones show signs typical of dynamo action based on the usual helicity effect. In the idealized simulations without rotation and just shear the above correlation is found to be particularly strong. In both cases there is, as expected, a systematic flux of magnetic helicity through the midplane. However, very little magnetic helicity leaves the domain through the top and bottom boundaries. The idealized simulations reveal that much of this systematic flux comes from the rotational component of the helicity flux and does not contribute to its divergence.
Abstract: We present numerical simulations of three-dimensional compressible magnetoconvection in a rotating rectangular box that represents a section of the solar convection zone. The box contains a convectively unstable layer, surrounded by stably stratified layers with overshooting convection. The magnetic Reynolds number, Rm, is chosen subcritical, thus excluding spontaneous growth of the magnetic field through dynamo action, and the magnetic energy is maintained by introducing a constant magnetic field into the box, once convection has attained a statistically stationary state. Under the influence of the Coriolis force, the advection of the magnetic field results in a non-vanishing contribution to the mean electric field, given by (u x b). From this electric field, we calculate the alpha -effect, separately for the stably and the unstably stratified layers, by averaging over time and over suitably defined volumes. From the variation of alpha we derive an error estimate, and the dependence of alpha on rotation and magnetic field strength is studied. Evidence is found for rotational quenching of the vertical alpha effect, and for a monotonic increase of the horizontal alpha effect with increasing rotation. For Rm approximate to 30, our results for both vertical and horizontal alpha effect are consistent with magnetic quenching by a factor [1 + Rm(B-o/B-eq)(2)](-1). The signs of the small-scale current helicity and of the vertical component of alpha are found to be opposite to those for isotropic turbulence.
Abstract: We consider the effect of vertical outflows on the mean-field dynamo in a thin disk. These outflows could be due to winds or magnetic buoyancy. We analyse both two-dimensional finite-difference numerical solutions of the axisymmetric dynamo equations and a free-decay mode expansion using the thin-disk approximation. Contrary to expectations, a vertical velocity can enhance dynamo action! provided the velocity is not too strong. In she nonlinear regime this can lead to super-exponential growth of the magnetic field.
Abstract: The evolution of magnetic fields is studied using simulations of forced helical turbulence with strong imposed shear. After some initial exponential growth, the magnetic field develops a large-scale travelling wave pattern. The resulting field structure possesses magnetic helicity, which is conserved in a periodic box by the ideal magnetohydrodynamics equations and can hence only change on a resistive time-scale. This strongly constrains the growth time of the large-scale magnetic field, but less strongly constrains the length of the cycle period. Comparing this with the case without shear, the time-scale for large-scale field amplification is shortened by a factor Q, which depends on the relative importance of shear and helical turbulence, and which also controls the ratio of toroidal to poloidal field. The results of the simulations can be reproduced qualitatively and quantitatively with a mean-field alpha Omega -dynamo model with alpha-effect and turbulent magnetic diffusivity coefficients that are less strongly quenched than in the corresponding a alpha (2)-dynamo.
Abstract: The buoyant rise of thermals (i.e. bubbles of enhanced entropy, but initially in pressure equilibrium) is investigated numerically in three dimensions for the case of an adiabatically stratified layer covering 6-9 pressure scale heights. It is found that these bubbles can travel to large heights before being braked by the excess pressure that builds up in order to drive the gas sideways in the head of the bubble. Until this happens, the momentum of the bubble grows ass described by the time-integrated buoyancy force. This validates the simple theory of bubble dynamics whereby the mass entrainment of the bubble provides an effective braking force well before the bubble stops ascending. This is quantified by an entrainment parameter alpha which is calculated from the simulations and is found to he in good agreement with the experimental measurements. This work is discussed in the context of contact binaries whose secondaries could be subject to dissipative heating in the outermost layers.
Abstract: We study the effects of vertical outflows on mean-field dynamos in disks. These outflows could be due to thermal winds or magnetic buoyancy. We analyse numerical solutions of the nonlinear mean-field dynamo equations using a two-dimensional finite-difference model. Contrary to expectations, a modest vertical velocity can enhance dynamo action. This can lead to super-exponential growth of the magnetic field and to higher magnetic energies at saturation in the nonlinear regime.
Abstract: Dynamo action is investigated in simulations of locally isotropic and homogeneous turbulence in a slab between open boundaries. It is found that a "pseudo-vacuum" boundary condition (where the field is vertical) leads to strong helicity fluxes which significantly reduce the amplitude of the resulting large-scale field. On the other hand, if there is a conducting halo outside the dynamo-active region, the large scale field amplitude can reach larger values, but the time scale after which this field is reached increases linearly with the magnetic Reynolds number. In both cases, most of the helicity flux is found to occur on large scales. From the variety of models considered we conclude that open boundaries tend to lower the saturation field strength compared to the case with periodic boundaries. The rate at which this lower saturation field strength is attained is roughly independent of the strength of the turbulence and of the boundary conditions. For dynamos with less helicity, however, significant field strengths could be reached in a shorter time.
Abstract: The emergence of a large scale magnetic field from randomly forced isotropic strongly helical flows is discussed in terms of the inverse cascade of magnetic helicity and the alpha-effect. In simulations of such flows the maximum field strength exceeds the equipartition field strength for large scale separation. However, helicity conservation controls the speed at which this final state is reached. In the presence of open boundaries magnetic helicity fluxes out of the domain are possible. This reduces the timescales of the field growth, but it also tends to reduce the maximum attainable field strength.
Abstract: We excite an epicyclic motion, the amplitude of which depends on the vertical position, z, in a simulation of a turbulent accretion disc. An epicyclic motion of this kind may be caused by a warping of the disc. By studying how the epicyclic motion decays, we can obtain information about the interaction between the warp and the disc turbulence. A high-amplitude epicyclic motion decays first by exciting inertial waves through a parametric instability, but its subsequent exponential damping may be reproduced by a turbulent viscosity. We estimate the effective viscosity parameter, alpha(v), pertaining to such a vertical shear. We also gain new information on the properties of the disc turbulence in general, and measure the usual viscosity parameter, alpha(h), pertaining to a horizontal (Keplerian) shear. We find that, as is often assumed in theoretical studies, alpha(v) is approximately equal to alpha(h) and both are much less than unity, for the field strengths achieved in our local box calculations of turbulence. In view of the smallness (similar to 0.01) of alpha(v) and alpha(h) we conclude that for beta = p(gas)/p(mag) similar to 10 the time-scale for diffusion or damping of a warp is much shorter than the usual viscous time-scale. Finally, we review the astrophysical implications.
Abstract: We consider non-linear transport and drift processes caused by an inhomogeneous magnetic field in a turbulent fluid. The coefficients of magnetic diffusivity and drift velocity are calculated by making use of the second-order correlation approximation. Transport processes in the presence of a sufficiently strong magnetic field become anisotropic with larger diffusion rate and turbulent electrical resistivity across the field than along the field. Non-linear effects also lead to a drift of the magnetic field away from the regions with a higher magnetic energy.
Abstract: It is shown that ambipolar diffusion as a useful model for nonlinearity leads to similar behaviour of large scale turbulent dynamos as full MHD. This is demonstrated using both direct simulations in a periodic box and a closure model for the magnetic correlation functions applicable to infinite space. Large scale fields develop via a nonlocal inverse cascade as described by the ct-effect. However, magnetic helicity can only change on a resistive timescale, so the time it takes to organize the field into large scales increases with magnetic Reynolds number.
Abstract: Dynamo theory is reviewed with particular emphasis on recent developments. There now seems to be a strong case for dynamo effects that are driven by the magnetic field itself. This is linked to recent interpretations of the observed stellar cycle periods which suggest that the ratio of cycle frequency to rotational frequency increases, up to some point, with stellar chromospheric activity. This ratio may be interpreted as a measure of the alpha-effect in dynamo theory, which would then increase with magnetic field strength. The important question of what happens as stars become fully convective is also addressed. It is argued that the dynamo does not work at the bottom of the convection zone, but in the entire convection zone proper. However, because of turbulent pumping effects the magnetic field is pushed to the bottom of the convection zone or, in the case of a fully convective star, to its center.
Abstract: We present a Green's function approach for quantifying the transport of a passive scalar (tracer) field in three-dimensional simulations of turbulent convection. Nonlocal, nondiffusive behavior is described by a transilient matrix (the discretized Green's function), whose elements contain the fractional tracer concentrations moving from one subvolume to another as a function of time. The approach was originally developed for and applied to geophysical flows, but here we extend the formalism and apply it in an astrophysical context to three-dimensional simulations of turbulent compressible convection with overshoot into convectively stable bounding regions. We introduce a novel technique to compute this matrix in a single simulation by advecting labeled particles rather than solving the passive scalar equation for a large number of different initial conditions. The transilient matrices thus computed are used as a diagnostic tool to quantitatively describe nonlocal transport via matrix moments and transport coefficients in a generalized, multiorder diffusion equation. Results indicate that transport in both the vertical and horizontal directions is strongly influenced by the presence of coherent velocity structures, generally resembling ballistic advection more than diffusion. The transport of a small fraction of tracer particles deep into the underlying stable region is reasonably efficient, a result which has possible implications for the problem of light-element depletion in late-type stars.
Abstract: We present a Green's function approach for quantifying the transport of a passive scalar (tracer) field in three-dimensional simulations of turbulent convection. Nonlocal, nondiffusive behavior is described by a transilient matrix (the discretized Green's function), whose elements contain the fractional tracer concentrations moving from one subvolume to another as a function of time. The approach was originally developed for and applied to geophysical flows, but here we extend the formalism and apply it in an astrophysical context to three-dimensional simulations of turbulent compressible convection with overshoot into convectively stable bounding regions. We introduce a novel technique to compute this matrix in a single simulation by advecting labeled particles rather than solving the passive scalar equation for a large number of different initial conditions. The transilient matrices thus computed are used as a diagnostic tool to quantitatively describe nonlocal transport via matrix moments and transport coefficients in a generalized, multiorder diffusion equation. Results indicate that transport in both the vertical and horizontal directions is strongly influenced by the presence of coherent velocity structures, generally resembling ballistic advection more than diffusion. The transport of a small fraction of tracer particles deep into the underlying stable region is reasonably efficient, a result which has possible implications for the problem of light-element depletion in late-type stars. PACS number(s): 47.27.-i.
Abstract: We present results from numerical simulations of magnetohydrodynamic turbulence in accretion discs. Our simulations show that the turbulent stresses that drive the accretion are less stratified than the matter; thus, the surface layers are more strongly heated than the interior of the disc.
Abstract: Local hydromagnetic simulations of accretion-disc turbulence currently provide the most convincing evidence that the origin of turbulence in discs could be the Balbus-Hawley magnetorotational instability. The main results of such calculations are highlighted with particular emphasis on the generation of large-scale magnetic fields. Comparison with mean-field dynamo theory is made. This theory is then used to address the question of the launching and collimation of winds emanating from the disc surfaces.
Abstract: A recent paper claims that the well known Cowling 'anti-dynamo' theorem is a "misconception", and that a simple axisymmetric sunspot model constitutes a counter example. We do not believe these claims to have been substantiated.
Abstract: Motivated by new observations of solar surface how patterns of mesogranulation, theoretical computations of the horizontal divergence-vorticity correlation are presented. Because of its close relation to the helicity in rotating turbulence such observations and discussions are of particular importance for the conventional dynamo theory. For the northern hemisphere we find a small, but always negative, divergence-vorticity correlation. Both an analytical Second Order Correlation Approximation for slow rotation as well as a numerical simulation (originally done for accretion disks) for fast rotation yield very similar results.
Abstract: We further explore nondimensional relationships between the magnetic dynamo cycle period P-eye, the rotational period P-rot, the activity level (as observed in Ca II HK), and other stellar properties by expanding the stellar sample studied in the first paper in this series. We do this by adding photometric and other cycles seen in active stars and the secondaries of CV systems and by selectively adding less certain cycles from the Mount Wilson HK survey; evolved stars, long-term HK trends and secondary P-eye are also considered. We confirm that most stars with age t greater than or similar to 0.1 Gyr occupy two roughly parallel branches, separated by a factor of similar to 6 in P-eye, with the ratio of cycle and rotational frequencies omega(eye)/Omega proportional to Ro(-0.5), where Ro is the Rossby number. Using the model of the first paper in this series, this result implies that the alpha effect increases with mean magnetic field (contrary to the traditional alpha-quenching concept) and that alpha and omega(eye) decrease with t. Stars are not strictly segregated onto one or the other branch by activity level, though the high-omega(eye)/Omega branch is primarily composed of inactive stars. The expanded data set suggests that for t greater than or similar to 1 Gyr, stars can have cycles on one or both branches, though among older stars, those with higher (lower) mass tend to have their primary P-eye on the lower (upper) omega(eye)/Omega branch. The Sun's similar to 80 yr Gleissberg cycle agrees with this scenario, suggesting that longterm activity "trends" in many stars may be segments of long (P-eye similar to 50-100 yr) cycles not yet resolved by the data. Most very active stars (P-rot < 3 days) appear to occupy a new, third branch with omega(eye)/Omega proportional to Ro(0.4). Many RS CVn variables lie in a transition region between the two most active branches. We compare our results with various models, discuss their implications for dynamo theory and evolution, and use them to predict P-eye for three groups: stars with long-term HK trends, stars in young open clusters, and stars that may be in Maunder-like magnetic minima.
Abstract: The evolution of a superbubble is simulated using a local three-dimensional, non-ideal MHD model, which includes galactic differential rotation, an external gravitational potential, heating via supernova explosions and radiative cooling of the interstellar medium (TSM). In our model a superbubble is formed due to the clustering of supernova activity, mimicking an OB association. Supernovae are modelled as instantaneous explosions that release 10(51) erg of thermal energy and 3M(.) of gas in a small volume. We implement a superbubble with the luminosity 3 x 10(37) erg s(-1) into an initial TSM, which is taken from our earlier calculations modelling the warm and hot phases of the ISM. The simulated ISM has a multi-phase structure with hot, dilute and warm, denser gas coexisting in pressure equilibrium; there is also some cold, dense gas in the form of clouds and filaments arising from supernova compression. The multicomponent gas is in a state of developed turbulence, with r.m.s. velocity 10 and 40km s(-1) for the warm and hot gas, respectively At the developed state of the simulation there is a magnetic field of 1.3 mu G strength having both uniform and random components. The evolution of a superbubble is rather different from that indicated by models with quasi-uniform ambient medium. The superbubble loses its spherical symmetry at very early stages of expansion. Its break-through from the disc is strongly facilitated by the nonuniformity of its environment. A superbubble which would be confined in the disc according to criteria obtained for a quasi-uniform ISM can break. out to the halo.
Abstract: There are now several simulations showing the generation of large scale magnetic fields whose energy exceeds the kinetic energy of the turbulence. Those simulations have in common that the large scale field generation is related to some kind of a magnetic instability (magnetorotational instability, magnetic buoyancy instability and in some cases even the kink instability). The large scale field generation sets in after some level of small scale dynamo activity has been established, suggesting that the large scale field generation is essentially nonkinematic. This mechanism is also essentially anisotropic, because the various instabilities mentioned above do not exist under isotropic conditions (shear, rotation and gravity are needed). Some aspects of the field generation are reproduced by ct-effect dynamos, which can be compared with observations.
Abstract: The drag force experienced by a gravitational body moving in a straight-line trajectory through a homogeneous isothermal gaseous medium of given sound speed is investigated numerically. For perturbers with constant velocity, linear theory describes successfully the temporal evolution and magnitude of the force. The result obtained recently by E. Ostriker-that for Mach numbers M = 1-2 the force is stronger in a gaseous medium than in a collisionless medium, as described by the standard Chandrasekhar formula-is confirmed. The corresponding minimum impact radius r(min) for a body described with a Plummer model with core radius R-soft is r(min)/R-soft approximate to 2.25. When M<1, the drag force is strongly suppressed, which is consistent with Ostriker's results but in disagreement with the Chandrasekhar formula. However, when the perturber is decelerated by its own wake to M<1, the effective drag force remains initially somewhat larger than the value in the case of constant velocity because it takes some time to get rid of the wake that was generated during its supersonic history.
Abstract: Numerical evidence for a finite-time singularity in ideal 3D magnetohydrodynamics is presented. The simulations start from two interlocking magnetic flux rings with no initial velocity. Curvature shrinks the rings until they touch and current sheets form between them. The evidence for a singularity in a finite time t(c) is that the peak current density behaves like \\J\\(infinity) similar to 1/(t(c) - t) for a range of sound speeds and initial conditions. For the incompressible calculations \\omega\\(infinity)/\\J\\(infinity) --> const. In resistive reconnection the magnetic helicity is nearly conserved while energy is dissipated.
Abstract: The dynamic state of the interstellar medium, heated and stirred by supernovae (SNe), is simulated using a three-dimensional, nonideal MHD model in a domain extended 0.5 x 0.5 kpc horizontally and 2 kpc vertically, with the gravitational field symmetric about the midplane of the domain, z = 0. We include both Type I and Type II SNe, allowing the latter to cluster in regions with enhanced gas density. The system segregates into two main phases: a warm, denser phase and a hot, dilute gas in global pressure equilibrium; there is also dense, cool gas compressed into filaments, shells, and clumps by expanding SN remnants. The filling factor of the hot phase grows with height, so it dominates at \z\ greater than or similar to 0.5 kpc. The multicomponent structure persists throughout the simulation, and its statistical parameters show little time variation. The warm gas is in hydrostatic equilibrium, which is supported by thermal and turbulent pressures. The multiphase gas is in a state of developed turbulence. The rms random velocity is different in the warm and hot phases, 10 and 40 km s(-1), respectively, at \z\ less than or similar to 1 kpc; the turbulent cell size (twice the velocity correlation scale) is about 60 pc in the warm phase.
Abstract: We study the changes in the dynamical behaviour of axisymmetric spherical mean-field dynamo models produced by changes in their geometry and topology, by considering a two parameter family of models, ranging from a full sphere to spherical shell, tents and disc-like configurations, within a unified framework. We find that the two parameter space of the family of models considered here separates into at least three different regions with distinct characteristics for the onset of dynamo action. In two of these regions, the most easily excited fields are oscillatory, in one case with dipolar symmetry, and in the other with quadrupolar, whereas in the third region the most easily excited field is steady and quadrupolar. In the nonlinear regime, we find that topological changes can alter significantly the dynamical behaviour, whilst modest changes in geometry can produce qualitative changes, particularly for thin disc-like configurations. This is of potential importance, since the exact shapes of astrophysical bodies, especially accretion discs and galaxies, are usually not precisely known.
Abstract: The mean electromotive force is considered in a differentially rotating fluid taking into account stretching of the turbulent magnetic field. Calculations are performed by making use of the second order correlation approximation. Nonuniformity of the angular velocity leads to specific drift processes in the azimuthal direction. Due to this drift the magnetic field can rotate with a somewhat different angular velocity than the fluid. Differential rotation can also lead in a new instability of a non-axisymmetric mean held. Regardless of the law of the differential rotation this instability can result in an exponential amplification of the field.
Abstract: The possibility of dynamo action resulting from a pair of elongated vortex structures immersed in an electrically conducting fluid is investigated. For elongated vortex structures, the critical magnetic Reynolds number for dynamo action is about half that for the spherical rotors that have been studied previously. When applied to Kolmogorov turbulence with vortex structures of scale comparable to the dissipation length, this model can explain dynamo action only when the magnetic Prandtl number (=kinematic viscosity/magnetic diffusivity) exceeds a critical value that is larger than unity. It is argued that in astrophysical bodies where this condition is not satisfied (in stellar convection zones, for example), dynamo action must instead result from motions on all scales up to the size of the region. (C) 1999 American Institute of Physics. [S1070-664X(99)01001-0].
Abstract: The stability properties of magnetized discs rotating with angular velocity Omega = Omega(s,z), dependent on both the radial and the vertical coordinates s and z, are considered. Such a rotation law is adequate for many astrophysical discs (e.g., galactic and protoplanetary discs, as well as accretion discs in binaries). In general, the angular velocity depends on height, even in thin accretion discs. A linear stability analysis is performed in the Boussinesq approximation, and the dispersion relation is obtained for short-wavelength perturbations. Any dependence of Omega on z can destabilize the flow. This concerns primarily small-scale perturbations for which the stabilizing effect of buoyancy is strongly suppressed due to the energy exchange with the surrounding plasma. For a weak magnetic field, instability of discs is mainly associated with vertical shear, whilst for an intermediate magnetic field the magnetic shear instability, first considered by Chandrasekhar and Velikhov, is more efficient. This instability is caused by the radial shear which is typically much stronger than the vertical shear. Therefore the growth time for the magnetic shear instability is much shorter than for the vertical shear instability. A relatively strong magnetic field can suppress both these instabilities. The vertical shear instability could be the source of turbulence in protoplanetary discs, where the conductivity is low.
Abstract: We consider turbulence generated by galaxies moving transonically through the intracluster gas. We show that neither the gravitational drag nor the gas stripping from the galaxies are able, by themselves, to generate turbulence at a level required to feed the dynamo in the intracluster gas. Some implications for cluster radio halos are discussed.
Abstract: We investigate the general properties of supernova driven interstellar turbulence using local three-dimensional MHD simulations under Galactic conditions. Our model includes the effects of large-scale shear due to Galactic differential rotation, density stratification, compressibility, magnetic fields, heating via supernova explosions and parameterized radiative cooling of the interstellar medium. In addition to investigating isolated supernova explosions we allow for multiple supernovae distributed randomly in the Galactic disc and exponentially in the vertical direction. Single supernova explosions drive a strong shock, the lifetime of which is approximately 2 Myr in our model. This stage is found to be characterized by a kinetic energy spectrum in the diffuse gas with spectral index consistent with k = -2. Large-scale shear and Coriolis force act on the supernova remnant producing some vorticity inside it, but this process was found to be very weak. lit the case of multiple supernova explosions, older remnants have an important role causing density fluctuations in the interstellar medium. In this "clumpy" medium, the propagation velocity of the shock fronts changes due to the changing density, and vorticity is generated. In the absence of these supernova interactions the kinetic energy spectrum shows a relatively wide shock spectrum with spectral index k = -2, but when the supernova interactions become dominant the classical k = -5/3 spectrum is observed.
Abstract: Calculations for mean field dynamo models (in both full spheres and spherical shells), with both algebraic and dynamic alpha-quenchings, show qualitative as well as quantitative differences and similarities in the dynamical behaviour of these models. We summarise and enhance recent results with extra examples. Overall, the effect of using a dynamic a appears to be complicated and is affected by the region of parameter space examined.
Abstract: Three-dimensional simulations of a thermally stably stratified gas with a localized layer of toroidal magnetic field are carried out. The magnetic field gives rise to a magnetic buoyancy instability. Due to the presence of rotation the resulting fluid motions are helical and lead to an alpha-effect, i.e. to a component of the electromotive force in the direction of the mean magnetic field. The value of alpha is estimated during the exponential growth phase of the instability. The mean vertical transport velocity of the magnetic field is also calculated. It is found that alpha varies with latitude and its value is positive in the northern hemisphere.
Abstract: The radial structure of a thin accretion disc is calculated in the presence of a central dipole magnetic field aligned with the rotation axis. The problem is treated using a modified expression for the turbulent magnetic diffusion, which allows the angular momentum equation to be integrated analytically. The governing algebraic equations are solved iteratively between 1 and 10(4) stellar radii. An analytic approximation is provided that is valid near the disruption radius at about 100 stellar radii. At that point, which is approximately 60 per cent of the Alfven radius and typically about 30 per cent of the corotation radius, the disc becomes viscously unstable. This instability results from the fact that both radiation pressure and opacity caused by electron scattering become important. This in turn is a consequence of the magnetic field which leads to an enhanced temperature in the inner parts. This is because the magnetic field gives rise to a strongly enhanced vertically integrated viscosity, so that the viscous torque can balance the magnetic torque.
Abstract: We study axisymmetric mean field spherical and spherical shell dynamo models, with both dynamic and algebraic alpha-quenchings. Our results show that there are qualitative as well as quantitative differences and similarities between these models. Regarding similarities, both groups of models exhibit symmetric, antisymmetric and mixed modes of behaviour. As regards differences, the important feature in the full sphere models is the occurrence of chaotic behaviour in the algebraic alpha-quenching models. For the spherical shell models with dynamic alpha the main features include the possibility of multi-attractor regimes with final state sensitivity with respect to small changes in the magnitude of alpha and the initial parity. We find the effect of introducing a dynamic alpha is likely to be complicated and depend on the region of the parameter space considered, rather than a uniform change towards simplicity or complexity.
Abstract: Axisymmetric mean-field dynamo models in spherical shells are shown to be capable of producing temporally intermittent behaviour. This is of potential importance since (i) it is, as far as we are aware, the first time such behaviour has been produced internally by a mean-field dynamo model in a spherical shell, without requiring any additional assumptions or truncations, and (ii) it may be characteristic of the type of behaviour observed in the long-term record of solar activity, such as Maunder minima. We also show that these types of behaviour persist when the functional form of the alpha quenching is altered and also occur over intervals of the shell thickness and the dynamo number.
Abstract: We propose a new interpretation of the relationships between the dynamo cycle period (P-cyc) as observed in Ca II H and K, the rotational period (P-rot), the activity level, and other stellar properties. Viewed within this framework, the data suggest that the dynamo alpha-parameter increases with magnetic field strength, contrary to the conventional idea of alpha-quenching. The data also suggest a possibly discontinuous dependence of the ratio of cycle to rotation frequency, omega(cyc)/Omega, as a function of Rossby number, Ro (or equivalently, activity or age). Stars evolve with omega(cyc)/Omega proportional to t(-0.35) (or RO-0.7), Until age t approximate to 2-3 Gyr (roughly at the Vaughan-Preston gap), where a sharp transition occurs, in which omega(cyc)/Omega increases by a factor of approximate to 6. Thereafter, evolution with omega(cyc)/Omega proportional to t(-0.35) continues. The age at which transition occurs may be mass dependent, with K stars making the transition first.
Abstract: It is shown that the cross-helicity effect facilitates rapid growth of the large scale magnetic field in young galaxies. This field then acts as a seed for the standard alpha Omega-type dynamo at later stages. This mechanism may be responsible for the relatively strong magnetic fields observed in young high redshift galaxies.
Abstract: The formation of planetesimals is investigated by studying the transport of dust particles in a local three-dimensional simulation of accretion disc turbulence. Heavy particles fall rapidly towards the midplane, whereas lighter particles are strongly advected by the flow. For light particles the turbulence leads to a rapid redistribution of particles such that their density per unit mass is approximately constant with height. There is no pronounced concentration of particles in vortices or anticyclones, as was suggested previously. This is partly because of the adverse effect of keplerian shear and also because in our simulation vortices are only short lived. However, if we assume the gas velocity to be frozen in time, there is a concentration of dust in ring-like structures after a few orbits. This is caused mainly by a convergence of the gas flow in those locations, rather than the presence of vortices or anticyclones.
Abstract: The Herzenberg dynamo, consisting of two rotating electrically conducting spheres with non-parallel spin axes, immersed in a finite spherical conducting medium, is simulated numerically for a variety of parameters not accessible to the original asymptotic theory. Our model places the spheres in a spatially periodic box. The largest growth rate is obtained when the angle, cp, between the spin axes is somewhat larger than 125 degrees. In agreement with the asymptotic analysis, it is found that the critical dynamo number is approximately proportional to the cube of the ratio of the common radius of the spheres and their separation. The asymptotic prediction, strictly valid only in the limit of small spheres, remains approximately valid even when the diameter of the spheres becomes comparable to their separation. For /phi/ < 90 degrees we also find oscillatory solutions, which were not predicted by Herzenberg's analysis. To understand such solutions we present a modified asymptotic analysis in which the separation of the two spheres is essentially replaced by the skin depth which, in turn, depends on the diameter of the spheres. The magnetic field consists of magnetic flux rings wrapped around the two spheres. Applications to local models of turbulent dynamos and to dynamo action in binary stars are discussed.
Abstract: Coherent structures in turbulent flows consisting of vorticity filaments may generate small-scale magnetic fields by means of dynamo action with a mechanism similar to that known as the Herzenberg dynamo. In order to analyse the consequences of this assumption for the properties of the resulting magnetic field, we have performed numerical simulations for a Herzenberg-like model system with a prescribed flow, and determined the critical magnetic Reynolds number Hz for the dynamo. The critical value is of the order of a few hundred and is to be compared with the local magnetic Reynolds number for a pair of vortex filaments, calculated as a function of the Reynolds number of the flow by means of a scaling argument following Kolmogorov theory. This gives us fairly stringent conditions on the magnetic Prandtl number. Pr-M has to be large, of the order of a few hundred. The resulting magnetic field has a scale comparable with the diameter of the vorticity tubes and is thus of small-scale, compared to the integral scale of the flow.
Abstract: In a recent work (Covas et al., 1996), the behaviour and the robustness of truncated alpha Omega dynamos with a dynamic alpha were studied with respect to a number of changes in the driving term of the dynamic alpha equation, which was considered previously by Schmalz and Stir (1991) to be of the form similar to A phi B phi Here we review and extend our previous work and consider the effect of adding a quadratic quenching term of the form alpha\B\(2). We find that, as before, such a change can have significant effects on the dynamics of the related truncated systems. We also find intervals of(negative) dynamo numbers, in the system considered by Schmalz and Stix (1991), for which there is sensitivity with respect to small changes in the dynamo number and the initial conditions, similar to what was found in our previous work. This latter behaviour may be of importance in producing the intermittent type of behaviour observed in the Sun.
Abstract: We use the mean-held dynamo equations to show that spatially and temporally incoherent fluctuations in the helicity in mirror-symmetric turbulence in a shearing flow can generate a large-scale, coherent magnetic field. We illustrate this effect with simulations of a few simple systems. For statistically homogeneous turbulence, we find that the dynamo growth rate is roughly tau(eddy)(-1/3)tau(shear)(-2/3)N(eddy)(-1/3)(lambda(eddy)/L(B))(2/3), where tau(eddy) is the eddy turnover time, tau(shear)(-1) is the local shearing rate, N-eddy is the number of eddies per magnetic domain, lambda(eddy) is the size of an eddy, and L(B) is the extent of a magnetic domain perpendicular to the mean flow direction. Even in the presence of turbulence and shear the dynamo can be stopped by turbulent dissipation if (for example) the eddy scale is close to the magnetic domain scale and tau(shear) > tau(eddy). We also identify a related incoherent dynamo in a system with a stationary distribution of helicity with a high-spatial frequency and an average value of zero. In accretion disks, the incoherent dynamo can lead to axisymmetric magnetic domains the radial and vertical dimensions of which will be comparable to the disk height. This process may be responsible for dynamo activity seen in simulations of dynamo-generated turbulence involving, for example, the Balbus-Hawley instability. However, although it explains the generation of a magnetic field in numerical simulations without significant large-scale average helicity and the occasional field reversals, it also predicts that the dimensionless viscosity will scale as similar to (h/r)(2), which is not seen in the simulations. On the other hand, this result is consistent with phenomenological models of accretion disks, although these suggest a slightly shallower dependence on h/r. We discuss some possible resolutions to these contradictions.
Abstract: Some recent results are reviewed that lead us now to believe that accretion discs are basically always magnetised. The main components are Balbus-Hawley and Parker instabilities on the one hand and a dynamo process on the other. A mechanical model for the Balbus-Hawley instability is presented and analysed quantitatively. Three-dimensional simulations are discussed, especially the resulting magnetic field structure. Possibilities of reproducing the held by an alpha Omega dynamo are investigated, especially its symmetry with respect to the midplane.
Abstract: We study the effects of plasma viscosity on the dynamics of primordial magnetic fields by simulating magnetohydrodynamics in the early universe by appropriate non-linear cascade models, We find numerically that even in the presence of large kinetic viscosity, magnetic energy is transferred to large length scales. There are indications, however, that the inverse cascade stops at a given time which depends on the magnitude of viscosity. For realistic viscosities We do not find equipartition between magnetic and kinetic energies.
Abstract: We use data from numerical simulations of dynamo-generated turbulence in the shearing box approximation to determine the dynamo alpha-effect and its dependence on the rotation law Omega(r). The data suggest that the dynamo alpha is not simply proportional to the local angular velocity Omega(r), as is usually assumed, but rather is proportional to the local Vorticity omega(r) = r(-1)d/dr(Omega r(2)). We also find tentative evidence to support the proposition that the backreaction of the magnetic field on a sets in when the field reaches equipartition with the energy in the turbulent motions. Furthermore, we propose an explanation as to why the sign of a is found to be opposite to that in the standard picture.
Abstract: There is phenomenological evidence that magnetic reconnection operates in the interstellar medium, and magnetic reconnection is also necessary for the operation of a galactic dynamo. The extremely long ohmic diffusion times of magnetic fields in typical interstellar structures suggest that reconnection occurs in two stages, with thin current layers that have relatively short resistive decay times forming by magnetohydrodynamical processes first, followed by reconnection of the fields in the layers. We propose that ambipolar drift can lead to the formation of these thin sheets in weakly ionized interstellar gas and can delineate the parameter regime in which this occurs by means of a numerical model: we find that the magnetic field cannot be too large and the medium cannot be too diffusive. Both limits are imposed by the requirement that the field be wound up about 1 time by the eddy.
Abstract: We investigate the behaviour of alpha Omega dynamos with a dynamic alpha, whose evolution is governed by the imbalance between a driving and a damping term. We focus on truncated versions of such dynamo models which are often studied in connection with solar and stellar variability. Given the approximate nature of such models, it is important to study how robust they are with respect to reasonable changes in the formulation of the driving and damping terms. For each case, we also study the effects of changes of the dynamo number and its sign, the truncation order and initial conditions. Our results show that changes in the formulation of the driving term have important consequences for the dynamical behaviour of such systems, with the detailed nature of these effects depending crucially on the form of the driving term assumed, the value and the sign of the dynamo number and the initial conditions. On the other hand, the change in the damping term considered here seems to produce little qualitative effect.
Abstract: Keplerian sheer flows are unstable towards a magnetic sheer instability that generates turbulence. The turbulence is considered to be a likely source for viscosity in accretion discs. Recently several groups have simulated this turbulence in order to estimate the strength of the turbulent viscosity. There are however significant quantitative discrepancies between their results. Estimates of the effective (Shakura-Sunyaev) viscosity parameter due to the magnetic field, <(alpha)over tilde>(SS) = -[BxBy/mu(0)p] (i.e. the ratio of Maxwell stress to gas pressure) ranges from 0.001 to 0.7. We verify these differences using the same code for all simulations, and show that the higher values of <(alpha)over tilde>(SS) are the result of an applied vertical magnetic field, Without an applied field the typical value is 0.005.
Abstract: The kinematic evolution of axisymmetric magnetic and electric fields is investigated numerically in Kerr geometry for a simplified Keplerian disk near a rotating black hole. In the cases investigated it is found that a magnetic field cannot be sustained against ohmic diffusion. In flat space this result is known as Cowling's antidynamo theorem. No support is found for the possibility that the gravitomagnetic dynamo effect of Khanna & Camenzind could lead to self-excited axisymmetric solutions. In practice, therefore, Cowling's antidynamo theorem may still hold in Kerr geometry, although here the original proof can no longer be applied.
Abstract: We use three-dimensional simulations to study compressible convection in a rotating frame with magnetic fields and overshoot into surrounding stable layers. The, initially weak, magnetic field is amplified and maintained by dynamo action and becomes organized into flux tubes that are wrapped around vortex tubes. We also observe vortex buoyancy which causes upward flows in the cores of extended downdraughts. An analysis of the angles between various vector fields shows that there is a tendency for the magnetic field to be parallel or antiparallel to the vorticity vector, especially when the magnetic field is strong. The magnetic energy spectrum has a short inertial range with a slope compatible with k(+1/3) during the early growth phase of the dynamo. During the saturated state the slope is compatible with k(-1). A simple analysis based on various characteristic timescales and energy transfer rates highlights important qualitative ideas regarding the energy budget of hydromagnetic dynamos.
Abstract: We investigate hydromagnetic turbulence of primordial magnetic fields using magnetohydrodynamics (MHD) in an expanding universe. We present the basic, covariant MHD equations, find solutions for MHD waves in the early universe, and investigate the equations numerically for random magnetic fields in two spatial dimensions. We find the formation of magnetic structures at larger and larger scales as time goes on. In three dimensions we use a cascade (shell) model that has been rather successful in the study of certain aspects of hydrodynamic turbulence. Using such a model we find that after similar to 10(9) times the initial time the scale of the magnetic field fluctuation (in the comoving frame) has increased by 4-5 orders of magnitude as a consequence of an inverse cascade effect (i.e., transfer of energy from smaller to larger scales). Thus at large scales primordial magnetic fields are considerably stronger than expected from considerations which do not take into account the effects of MHD turbulence.
Abstract: We estimate the Shakura-Sunyaev viscosity parameter alpha for different values of the shear/vorticity ratio, sigma/omega, using local simulations of dynamo-generated turbulence. We find that the time average of alpha is approximately proportional to sigma/omega (at least for sigma/omega < 10). We point out that this result may have important implications for the properties of thick accretion discs, because there omega is small and alpha would then tend to be large. Our result may also be important for accretion discs around black holes, because sigma/omega becomes large in the inner 10 Schwarzschild radii as a result of relativistic effects.
Abstract: Dynamo-generated turbulence is simulated in a modified shearing box approximation that removes scale invariance and allows finite accretion rates for a given distance from the central object. The effective Shakura-Sunyaev viscosity parameter, alpha(ss), is estimated in three different ways using the resulting mass accretion rate, the heating rate, and the horizontal components of the Maxwell and Reynolds stress tensors. The results are still resolution dependent: doubling the resolution leads to 1.4-1.6 times larger values for the viscosity parameter. For 63 x 127 x 64 meshpoints we find that alpha(ss) = 0.007.
Abstract: We discuss current observational and theoretical knowledge of magnetic fields, especially the large-scale structure in the disks and halos of spiral galaxies. Among other topics, we consider the enhancement of global magnetic fields in the interarm regions, magnetic spiral arms, and representations as superpositions of azimuthal modes, emphasizing a number of unresolved questions. It is argued that a turbulent hydromagnetic dynamo of some kind and an inverse cascade of magnetic energy gives the most plausible explanation for the regular galactic magnetic fields. Primordial theory is found to be unsatisfactory, and fields of cosmological origin may not even be able to provide a seed field for a dynamo. Although dynamo theory has its own problems, the general form of the dynamo equations appears quite robust. Finally, detailed models of magnetic field generation in galaxies, allowing for factors such as spiral structure, starbursts, galactic winds, and fountains, are discussed and confronted with observations.
Abstract: We examine the stability of the dynamical behaviour of axisymmetric alpha(2) omega dynamo models in rotating spherical shells as well as in spheres. Overall, our results show that the spherical dynamo models are more stable in the following senses: spherical models (i) do not seem to allow chaotic behaviour and (ii) are robust with respect to changes in the functional form of alpha. On the other hand, spherical shell models (i) are capable of producing chaotic behaviour for certain ranges of parameter values and (ii) possess, in the combined ''space'' of parameters and boundary conditions, regions of complicated behaviours, in the sense that there are regimes in which small changes in either the dynamo parameters or the boundary conditions can drastically change the qualitative behaviour of the model. Finally, we discuss briefly the physical relevance of our results.
Abstract: A simulation of hydromagnetic turbulence exhibiting dynamo action is employed to estimate the generalized entropies, H-q, from the distribution of moments of local expansion factors of material line elements. These generalized entropies can be used to characterize the dynamics of turbulence and of nonlinear dynamo action. The value of the metric entropy H-1, is comparable to the largest Lyapunov exponent describing the divergence of trajectories in phase space, which in turn is somewhat larger than the growth rate of the magnetic energy. The value of the topological entropy, H-0, is similar to the conversion rate of kinetic to magnetic energy, but larger than the growth rate of the dynamo. This is in agreement with results stating that the growth rate of the kinematic dynamo is limited by the topological entropy. The dependence of H-q on q leads to a criterion from which we infer that the degree of intermittency in our particular system is weak.
Abstract: The nonlinear evolution of magnetized Keplerian shear flows is simulated in a local, three-dimensional model, including the effects of compressibility and stratification. Supersonic flows are initially generated by the Balbus-Hawley magnetic shear instability. The resulting flows regenerate a turbulent magnetic field which, in turn, reinforces the turbulence. Thus, the system acts like a dynamo that generates its own turbulence. However, unlike usual dynamos, the magnetic energy exceeds the kinetic energy of the turbulence by a factor of 3-10. By assuming the field to be vertical on the outer (upper and lower) surfaces we do not constrain the horizontal magnetic flux. Indeed, a large-scale toroidal magnetic field is generated, mostly in the form of toroidal flux tubes with lengths comparable to the toroidal extent of the box. This large-scale held is mainly of even (i.e., quadrupolar) parity with respect to the midplane and changes direction on a timescale of similar to 30 orbits, in a possibly cyclic manner. The effective Shakura-Sunyaev alpha viscosity parameter is between 0.001 and 0.005, and the contribution from the Maxwell stress is similar to 3-7 times larger than the contribution from the Reynolds stress.
Abstract: We compute numerical solutions for axisymmetric, dynamically consistent mean-field dynamos in a spherical shell of conducting incompressible fluid. In the process of investigating the stability properties of solutions in the far-supercritical regime we found an unusual behaviour, with the magnetic energy decreasing discontinuously as the dynamo number is increased. A new stable solution with a more complicated field geometry emerges. In addition, a stable mixed parity state occurs at the discontinuity of the magnetic energy, between the two branches of stable pure parity solutions. For a given dynamo number there may be as many as four metastable solutions.
Abstract: We have computed mean field dynamo models in a deep spherical shell, without restriction on spatial symmetries, in which the growth of the magnetic field is limited solely by the back reaction of the large scale Lorentz force on the large scale motions. A parameterization of the Reynolds stress tenser is included to describe the generation of differential rotation. We find for moderate values of the Taylor number, when the differential rotation is also small, that the stable magnetic fields are nonaxisymmetric, with the same basic topology as a 'perpendicular dipole'. For larger Taylor numbers, and stronger absolute differential rotation, we expect axisymmetric fields to be stable. We briefly discuss the relevance of our results to the large scale nonaxisymmetric structures and extended starspots observed on late type 'active giant' and other stars.
Abstract: We consider the problem of how numerical simulations of convection in a spherical shell can be used to estimate turbulent transport coefficients that may be used in mean field theory. For this purpose we analyse data from simulations of three dimensional Boussinesq convection. The rotational influence on convection is described in terms of the LAMBDA-effect and anisotropic eddy conductivity. When the resulting transport coefficients are used in a mean field model, the original rotation law is recovered approximately. We thus conclude that the flow can be described in terms of a LAMBDA-effect. Our results are also compared with analytical theories and observations.
Abstract: The suggestion by several authors that the solar differential rotation is caused by a large scale instability of the basic convective state is examined. We find that the proposed mean-field models are unstable to a Rayleigh-Benard type instability, but argue that this cannot explain the differential rotation of the Sun, because such a flow would become nonaxisymmetric. We discuss the applicability of the mean-field equations to the problem.
Abstract: We present numerical results for mean-field alpha2OMEGA-dynamos in an accretion disk. We first study the linear case in both disks with constant thickness and disks with radially increasing thickness. The preferred mode is dipolar for a thick disk, but quadrupolar for a thin one. The quadrupolar mode generates a magnetic torque that transports angular momentum outwards. The role of the geometrical distribution of both the alpha-effect and the magnetic diffusivity in the disk is considered for thin disks. It is found that the parity of the most easily excited mode is unaffected, albeit the distribution of the magnetic field and torque change in such a way that a larger fraction of the field and the torque appears in regions with small diffusivity. For some interesting cases we study nonlinear effects like alpha-quenching and magnetic buoyancy. These effects can affect significantly the magnetic field distribution, compared to the linear case. A transition to chaotic behaviour is found for alpha-quenching when a is negative in the upper pan of the disk.
Abstract: We simulate numerically convection inside the solar convection zone under the influence of rotation at different latitudes. The computational domain is a small rectangular box with stress-free upper and lower boundaries, and with periodicity assumed in the lateral directions. We study the transport of angular momentum, which is important for the generation of differential rotation. The sign and the latitudinal dependence of the horizontal Reynolds stress component turn out to be in good agreement with correlation measurements of sunspot proper motions and with predictions from the theory of the LAMBDA-effect. We also investigate the other components of the Reynolds stress as well as the eddy heat flux tensor, both of which are needed in mean field models of differential rotation.
Abstract: We study several mean field dynamo models in disk geometry in an attempt to understand the origin of the nonaxisymmetric magnetic field present in M81. There appear to be three (at least) relevant mechanisms, which are not mutually exclusive. Because field growth times are not very short compared to galactic ages, a predominantly nonaxisymmetric seed field may still give a significantly nonaxisymmetric field after times of order 10(10) yr, even if the stable field configuration is axisymmetric. The spiral structure may give a non-axisymmetric structure to the disk turbulence, and thus to the turbulent coefficients appearing in mean field dynamo theory. Third, M81 may have undergone a close encounter with a companion galaxy. A dynamical model of the interaction predicts strong, nonaxisymmetric, large-scale gas velocities in the disk plane, and these can produce nonaxisymmetric fields. In the absence of the second of these effects, our models predict that nonaxisymmetric fields will be present in the outer parts of the galaxy, together with significant axisymmetric contributions in the inner part. However, we do not find that any of these effects, taken individually, can produce dominant nonaxisymmetric field structure. If they are simultaneously present, they can reinforce one another. Further, our calculations are for a relatively thick disk (thickness to radius ratio of order 0.2), and a reduction to smaller, and plausibly more realistic, values will also favor nonaxisymmetric field generation.
Abstract: We investigate the magnetic fields above the discs of spiral galaxies in the framework of axisymmetric nonlinear mean-field dynamo models for a disc surrounded by a spherical halo, using realistic rotation curves. We consider, in particular, NGC 4631 and NGC 89 1, and include turbulent diamagnetism, an anisotropy of the alpha effect and a galactic wind. In these models magnetic field is generated in a disc of scale height 1.5 kpc and distorted by the wind in the halo. For typical wind velocities of 50 ... 200 km/s in the halo we find good qualitative agreement between the observed polarisation maps and those synthesised from the magnetic fields of our models: Poloidal synthesised fields dominate in the halo of NGC 4631, and horizontal fields in that of NGC 89 1. In some cases, a galactic wind can enhance dynamo action, contrary to previous expectations. Our results indicate that turbulent diamagnetism plays an important role in galactic dynamos.
Abstract: We present calculations showing how both transient effects associated with nonaxisymmetric seed fields, and an interaction with a companion, can produce BSS type magnetic structure in a spiral galaxy.
Abstract: We discuss some aspects of the interrelationship between the dynamo problem for galaxies and their dynamics. First, we consider the generation of magnetic fields in the presence of fountain hows and galactic winds. Next, we discuss the distortion of a steady magnetic field by tidal effects and other transient spiral features. Finally, we give an expression for the amplitude of density waves generated by large-scale non-axisymmetric fields.
Abstract: Three-dimensional simulations of convection are studied with specific attention to the effects of rotation and latitude on different quantities. The latitude-dependence of the strength of convection is found to decrease with increasing strength of the turbulence. The Lambda-effect is, however, still present also in a more turbulent case.
Abstract: Two nonlinear dynamos have been analyzed by numerical means: 3D-simulation of the magneto-hydrodynamic equations and qualitative analysis of a simplified low-dimensional mean field model. It turns out that both are capable of deterministic chaos in a certain parameter range. As the basic tool the calculation of Lyapunov exponents has been used.
Abstract: Highly supercritical compressible convection is simulated in a two-dimensional domain in which the upper half is unstable to convection while the lower half is stably stratified. This configuration is an idealization of the layers near the base of the solar convection zone. Once the turbulent flow is well developed, a toroidal magnetic field B(tor) is introduced to the stable layer. The field's evolution is governed by an advection-diffusion-type equation, and the Lorentz force does not significantly affect the flow. After many turnover times the field is stratified such that \B(tor)\ / rho almost-equal-to constant in the convective layer, where rho is density, while in the stable layer this ratio decreases linearly with depth. Consequently most of the magnetic flux is stored in the overshoot layer. The inclusion of rotation leads to travelling waves which transport magnetic flux latitudinally in a manner reminiscent of the migrations seen during the solar cycle.
Abstract: Motivated by the observations that (i) the solar cycle is distinctly irregular on the long term, (ii) a proper treatment of the averaging processes of mean field theory yields stochastic terms that cannot be neglected in solar and stellar convection zones and (iii) the inclusion of parametrized nonlinearities in models with two spatial dimensions has not produced such irregular behaviour, we investigate the effects of various forms of noise on previously studied nonlinear alpha2omega dynamos in a sphere or a spherical shell. The study of the degree of fragility of the dynamo models in presence of stochastic perturbations is also interesting from a dynamical point of view. We investigate the consequences of perturbing solutions of both pure and mixed parity. In the former case we find that there can be quite pronounced deviations from the pure parity, and that these seem larger nearer to the relevant bifurcation. Effects are also stronger in a shell dynamo than in the full sphere. However, the magnetic period is relatively little changed in these examples. When a 2-torus solution (of mixed parity) is perturbed, the effects on the long period variations are much greater than on the short period, but even for quite strong perturbations the solutions do not leave the neighbourhood of the underlying attractor. We find our results to be robust, in that the precise nature of the noise term is qualitatively inconsequential; this is encouraging in view of the uncertainties present. We briefly contrast our results with those recently presented by Choudhuri for a model with one spatial dimension.
Abstract: The fractal dimension of iso-vorticity surfaces is estimated from a 3-dimensional simulation of homogeneous turbulence at moderate Reynolds numbers, performed by Vincent and Meneguzzi. The results are found to be compatible with a recently proposed theory which predicts a crossover from a 2-dimensional geometry at small scales to a fractal geometry at larger scales, with a dimension D = 2.5 + zeta/2, with zeta being the exponent characterizing the scaling of velocity differences.
Abstract: We present results from direct simulations of turbulent compressible hydromagnetic convection above a stable overshoot layer. Spontaneous dynamo action occurs followed by saturation, with most of the generated magnetic field appearing as coherent flux tubes in the vicinity of strong downdrafts, where both the generation and destruction of magnetic field is most vigorous. Whether or not this field is amplified depends on the sizes of the magnetic Reynolds and magnetic Prandtl numbers. Joule dissipation is balanced mainly by the work done against the magnetic curvature force. It is this curvature force which is also responsible for the saturation of the dynamo.
Abstract: We investigate linear and nonlinear dynamo models for a galactic disc embedded in a halo, assuming a relatively strong magnetic diffusivity and a non-vanishing alpha-effect in the halo. We take the halo to be spherical and embedded in a vacuum. The field is assumed to be axisymmetric, but we do not impose symmetry conditions at the equatorial plane. In one parameter regime we find mixed parity solutions. However, it is argued that the regular magnetic field in the galactic halo can hardly reach a steady-state configuration during the galactic lifetime. In the regime that is observably relevant the field can have an even parity within and near the disc and an odd one in the halo. This may have implications for explaining the occurrence of a neutral sheet above the galactic plane. During certain time intervals the rotation measure of these models shows a doubly peaked azimuthal variation, which could be falsely interpreted as an indication of a bisymmetric field structure.
Abstract: The energy cascade in both hydrodynamic and hydromagnetic Boussinesq convection is investigated at large Rayleigh numbers, using a scalar model for turbulence. Depending on the relative importance of direct and inverse transfer, either we observe classical Kolmogorov k-5/3 spectra or, if there is a strong inverse transfer of kinetic energy, we find a k-7/5 spectrum for the temperature fluctuation and a k-11/5 spectrum for the kinetic energy (Bolgiano-Obukhov scaling). We derive dissipative cutoff wave numbers that are consistent with these spectra.
Abstract: We extend previous investigations of axisymmetric, incompressible mean-field dynamos to the compressible case with strong stratification. We take thermodynamic effects into account using the anelastic approximation and show that the effects of stratification, compressibility and thermodynamics on the rotation law are small when we compare our results with those previously obtained for incompressible models. For solar values of the Taylor number cylindrical contours of the angular velocity typically occur - even for strong stratification. The stagnation line of the meridional circulation is close to the bottom of the convection zone. In the presence of magnetic fields the meridional flow is amplified, in particular close to the surface where the density is small and the Lorentz force per unit mass, J x B/rho, is large. The depth dependence of the magnetic energy density, however, is not much altered by the inclusion of a density stratification. For cyclical dynamo magnetic fields thermal and magnetic energies are approximately in antiphase. The cyclic variation in luminosity is small and it lags the variation in magnetic energy by approximately 1/8 of the period. For alpha partial derivative OMEGA/partial derivative r > 0 we find poleward migrating dynamo waves, whilst for alpha partial derivative OMEGA/partial derivative r < 0 our solutions are steady or oscillatory, depending on the boundary condition for the magnetic field at the bottom of the convection zone.
Abstract: The fractal nature of level sets and the multifractal nature of various scalar and vector fields in hydromagnetic and hydrodynamic turbulence are investigated using data of direct simulations. It turns out that fields whose evolution is governed by stretching terms (vortex stretching, magnetic-field line stretching) exhibit "near singularities" that result in a multifractal scaling. Such stretching terms can lead to a rapid increase in the local value of the field. Fields without rapid local increase have no multifractal scaling. Furthermore, the simulations support recent theoretical suggestions that the fractal properties of the level sets of various fields are quite insensitive to the existence of stretching. Indeed, all the fields under study (temperature, vorticity magnitude, magnetic-field magnitude) show rather universal behavior in the geometry of their level sets, consistent with a two-dimensional geometry at small scales, with a crossover to a universal fractal geometry at large scales. The dimension at large scales is compatible with the theoretical prediction of about 2.7. The most surprising result of the simulations is that it appears that the "near singularities" are not efficiently eliminated by viscous dissipation, but rather seem to be strongest at the Kolmogorov cutoff. The effects of the singularities do not quite penetrate into the inertial range. We offer a simple analytic model to account for this behavior. We conclude that our findings may be due to the relatively small Reynolds numbers, but may also be indicative of generic behavior at larger Reynolds numbers. We offer some thoughts about the expected scaling behavior in the inertial range in light of our findings.
Abstract: Calculations of mean field dynamos for galaxies have largely been for two rather disparate models. The thin disk model treats the ratio of disk height to radius explicitly as a small parameter, and applies zero tangential field boundary conditions at the disk surface. In contrast, the embedded disk model calculates the magnetic field in a spherical volume, whose radius is the disk radius and with the magnetic field fitting smoothly on to a curl-free exterior field at the surface of the sphere. The disk geometry is imposed by a flat distribution of the alpha-effect (and maybe also of the diffusivity eta). For computational reasons this model has not been applied to very thin disks, so the regions of validity of the two models are almost disjoint. Comparison between their predictions is therefore difficult. In this paper we calculate, in linear theory, galactic dynamo modes according to both thin and embedded (or "thick") disk models for a simple underlying distribution of alpha-effect and differential rotation, using a common numerical scheme. For the smallest attainable ratio of disk height to radius, we find the critical dynamo numbers are similar, but that there are some significant differences in field topology.
Abstract: We estimate the two largest Lyapunov exponents in a three-dimensional simulation of hydromagnetic convection in which there is dynamo action. It turns out that these first two exponents (from a total of 8 x 63(3)) are positive and of similar magnitude. Thus we conclude that the dynamo is chaotic. Furthermore, the consideration of local exponents helps in our understanding of the relevant dynamics. We find that the downdraft flows are more chaotic than the upward motions. Likewise, the velocity and magnetic fields have more chaotic dynamics than the temperature and density fields.
Abstract: Observational evidence for long-lived nonaxisymmetric features on the surfaces of rapidly rotating late-type giant stars (e.g. FK Comae and RS CVn stars) is beginning to be found. By analogy with sunspots, these features may be associated with large scale nonaxisymmetric magnetic field structures, generated by a dynamo operating in the convective envelopes. We describe a nonlinear nonaxisymmetric dynamo model, and show that for a simple 'alpha-quenching' nonlinearity together with suitable choices of underlying radial profiles of differential rotation and the alpha-effect, stable nonaxisymmetric solutions can be found by numerical integration.
Abstract: We investigate the influence of an azimuthally dependent alpha-effect on the properties of alpha-2 and alpha-2-OMEGA-dynamos in spherical geometry, restricting ourselves to odd parity solutions in linear theory. For all our linear models we find an exponentially growing mode, consisting of locked axisymmetric and nonaxisymmetric parts. A strong nonaxismmetry in alpha-substantially increases the linear growth rates at given dynamo number and can result in a marginal dynamo number that is significantly smaller than for an axisymmetric-alpha with the same value of integral-alpha-d V. We also report some exploratory nonlinear calculations and briefly discuss the relevance of our results to galactic dynamos and to stars.
Abstract: We present kinematic mean-field dynamo models for galaxies consisting of a turbulent gas disc embedded in a low-conductivity spherical halo. In the cases investigated an axisymmetric mode is the dominant one. This mode can be of either even or odd parity (S0 or A0, respectively). The preference of S0 or A0 modes is governed mainly by the radial profiles of the alpha effect and the turbulent magnetic diffusivity. If the gas disc extends into the galactic centre, the dominant mode is of A0 type and it is concentrated within the central region. If the model is changed so that induction effects are absent in the centre, the dominant mode is an axisymmetric spiral of even parity. We point out that a finite disc thickness and a low-conductivity halo will both lead to appreciable vertical magnetic fields outside the disc plane, and this may affect the interpretation of polarisation observations. We integrate the transfer equations for the three Stokes parameters I, Q, and U and produce in this way synthetic maps for the observed polarisation and rotation measures. Assuming a disc-like distribution of relativistic electrons, our models suggest that for moderate disc thickness modifications of the observed polarised emission due to fields above the plane are minor. For more extended electron distributions quite complicated polarisation patterns are obtained. Still, qualitatively the criteria distinguishing axisymmetric and bisymmetric spiral patterns remain valid.
Abstract: We discuss the observational results of cyclic variations of solar rotation and how these can be used as a means of probing the solar dynamo. We shortly describe two examples of dynamo models where the alpha-effect has been modified, and compare the resulting flows to the observations.
Abstract: We have studied axisymmetric nonlinear alpha-omega-dynamo models taking the interaction between even and odd parities fully into account. It turns out that the dominating type of symmetry is not always determined uniquely, but it can vary on a very long time scale compared to the period of the magnetic cycle. In some cases the frequency of this long term variation is close to the beat frequency of the two solutions with purely dipolar and purely quadrupolar parity. The occurrence of a second frequency is typical of solutions whose trajectory describes a torus in the phase space. We argue that this findings is of relevance for understanding secular variations observed in the Sun. For example measurements of sunspots indicate that the spot number on the northern hemisphere at present exceeds the number on the southern hemisphere. The reverse seems to have been the case at the end of last century.
