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1.
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2.
This article addresses the interesting and important problem of large-scale magnetic field generation in turbulent flows, using a self-consistent dynamo model recently developed. The main idea of this model is to consider the induction equation for the large-scale magnetic field, integrated consistently with the turbulent dynamics at smaller scales described by a magnetohydrodynamic shell model. The questions of dynamo action threshold, magnetic field saturation, magnetic field reversals, nature of the dynamo transition and the changes of small-scale turbulence as a consequence of the dynamo onset are discussed. In particular, the stability curve obtained by the model integration is shown in a very wide range of values of the magnetic Prandtl number not yet accessible by direct numerical simulation but more realistic for natural dynamos. Moreover, from our analysis it is shown that the large-scale dynamo transition displays a hysteretic behaviour and therefore a subcritical nature. The model successfully reproduces magnetic polarity reversals, showing the capability to generate persistence times which are increasing for decreasing magnetic diffusivity. Moreover, when the system reaches a statistically stationary dynamo state, where the large-scale magnetic field can abruptly reverse its polarity (magnetic reversal state) or not, keeping the same polarity (steady state), it shows an unmistakable tendency towards the energy equipartition for the turbulence at small scale.  相似文献   

3.
We determine the nonlinear drift velocities of the mean magnetic field and nonlinear turbulent magnetic diffusion in a turbulent convection. We show that the nonlinear drift velocities are caused by three kinds of the inhomogeneities; i.e., inhomogeneous turbulence, the nonuniform fluid density and the nonuniform turbulent heat flux. The inhomogeneous turbulence results in the well-known turbulent diamagnetic and paramagnetic velocities. The nonlinear drift velocities of the mean magnetic field cause the small-scale magnetic buoyancy and magnetic pumping effects in the turbulent convection. These phenomena are different from the large-scale magnetic buoyancy and magnetic pumping effects which are due to the effect of the mean magnetic field on the large-scale density stratified fluid flow. The small-scale magnetic buoyancy and magnetic pumping can be stronger than these large-scale effects when the mean magnetic field is smaller than the equipartition field. We discuss the small-scale magnetic buoyancy and magnetic pumping effects in the context of the solar and stellar turbulent convection. We demonstrate also that the nonlinear turbulent magnetic diffusion in the turbulent convection is anisotropic even for a weak mean magnetic field. In particular, it is enhanced in the radial direction. The magnetic fluctuations due to the small-scale dynamo increase the turbulent magnetic diffusion of the toroidal component of the mean magnetic field, while they do not affect the turbulent magnetic diffusion of the poloidal field.  相似文献   

4.
The turbulent cross helicity is directly related to the coupling coefficients for the mean vorticity in the electromotive force and for the mean magnetic-field strain in the Reynolds stress tensor. This suggests that the cross-helicity effects are important in the cases where global inhomogeneous flow and magnetic-field structures are present. Since such large-scale structures are ubiquitous in geo/astrophysical phenomena, the cross-helicity effect is expected to play an important role in geo/astrophysical flows. In the presence of turbulent cross helicity, the mean vortical motion contributes to the turbulent electromotive force. Magnetic-field generation due to this effect is called the cross-helicity dynamo. Several features of the cross-helicity dynamo are introduced. Alignment of the mean electric-current density J with the mean vorticity Ω , as well as the alignment between the mean magnetic field B and velocity U , is supposed to be one of the characteristic features of the dynamo. Unlike the case in the helicity or α effect, where J is aligned with B in the turbulent electromotive force, we in general have a finite mean-field Lorentz force J ?×? B in the cross-helicity dynamo. This gives a distinguished feature of the cross-helicity effect. By considering the effects of cross helicity in the momentum equation, we see several interesting consequences of the effect. Turbulent cross helicity coupled with the mean magnetic shear reduces the effect of turbulent or eddy viscosity. Flow induction is an important consequence of this effect. One key issue in the cross-helicity dynamo is to examine how and how much cross helicity can be present in turbulence. On the basis of the cross-helicity transport equation, its production mechanisms are discussed. Some recent developments in numerical validation of the basic notion of the cross-helicity dynamo are also presented.  相似文献   

5.
ABSTRACT

The magnetic fields in the inner parts of some spiral galaxies are understood quite well. Their generation is connected with the dynamo mechanism that is based on the joint action of turbulent diffusion and the α-effect. Usually the galactic dynamo is described with the so-called no-z approximation which takes into account that the galaxy disc is quite thin, with the implication that some spatial derivatives may be replaced by algebraic expressions. Some galaxies have outer rings that are situated at some distance from the galactic centre. The magnetic field can be described there also using the no-z model. As the thickness of such objects is comparable with their width, it is necessary to take into account the z-dependence of the field. We have studied the magnetic field evolution using the no-z approximation and torus dynamo model for the torus with rectangular cross-section in the axisymmetric case.  相似文献   

6.
A nonlinear mean field dynamo in turbulent disks and spherical shells is discussed. We use a nonlinearity in the dynamo which includes the effect of delayed back-reaction of the mean magnetic field on the magnetic part of the — effect. This effect is determined by an evolutionary equation. The axisymmetric case is considered. An analytical expression (in a single-mode approximation) is derived which gives the magnitude of the mean magnetic field as a function of rotation and the parameters for turbulent disks. The value obtained for the mean magnetic field is in agreement with observations for galaxies.  相似文献   

7.
The generation of magnetic fields in space plasmas and in astrophysics is usually described within the framework of magnetohydrodynamics. Turbulent helical flows produce magnetic fields very efficiently, with correlation length scales larger than those characterizing the flow. Within the context of the solar magnetic cycle, a turbulent dynamo is responsible for the so-called alpha effect, while the Omega effect is associated to the differential rotation of the Sun.We present direct numerical simulations of turbulent magnetohydrodynamic dynamos including two-fluid effects such as the Hall current. More specifically, we study the evolution of an initially weak and small-scale magnetic field in a system maintained in a stationary regime of hydrodynamic turbulence, and explore the conditions for exponential growth of the magnetic energy. In all the cases considered, we find that the dynamo saturates at the equipartition level between kinetic and magnetic energy, and the total energy reaches a Kolmogorov power spectrum.  相似文献   

8.
Abstract

The two dimensional incompressible MHD equations describing the decay of a random initial velocity field in the presence of a uniform magnetic background field are solved numerically by a Chebyshev spectral method. The nonlinear interactions of standing Alfvén-waves of a given energy are studied for various Reynolds numbers and field strengths of the magnetic background field. Small scale structures are generated by these interactions, which increase the energy dissipation, however, the uniform background field suppresses the production of arbitrary small scales. Thus energy dissipation is found to be insignificant at sufficiently high Reynolds numbers. Anisotropies of the fluctuating field components are also studied. In the temporal evolution they appear first in the magnetic field. This is explained by the conservation of mean square vector potential in the limit of infinite conductivity.  相似文献   

9.
We present simulations of the 3D nonlinear induction equation in order to investigate the temporal evolution of large-scale magnetic fields in spiral galaxies. Our model includes differential rotation, ambipolar diffusion and, based on small-scale turbulence, eddy diffusivity and the tensorial -effect with magnetic feedback. The nonaxisymmetric spiral pattern and – if considered – the vertical stratification of the galaxy are represented in its density and turbulence profile. Neglecting vertical stratification the lifetime and geometry of an initial magnetic field depend on the correlation time of interstellar turbulence corr . Short correlation times increase the lifetime of the initial magnetic field, but the field is rapidly wound up. Its pitch-angles develop to zero. The magnetic field has disappeared after at most 1 to 1.5 Gyr. A resonance like phenomenon is found by tuning the pattern velocity of the galactic spiral. The simulations then show an exceptional amplification of the magnetic field in the case that the pattern speed and a magnetic drift velocity have similar values. Considering a vertical stratification we achieve sufficiently long living grand-designed magnetic fields excited by dynamo action. The behaviour and geometry of the resulting field is again significantly influenced by the correlation time corr . Small values of corr lead to axisymmetric fields with small pitch-angles and field-concentration between the spiral arms. Increasing the correlation time the solutions show larger pitch-angles; and depending on very large correlation times the galactic dynamo rather generates fields clearly within the spiral arms and having a bisymmetric structure.  相似文献   

10.
We look at the large-scale dynamo properties of spatially periodic, time dependent, helical 2D flows of the form u(x, t)?=?(? y ?ψ?(x, y, t), ?? x ?ψ?(x, y, t), ?ψ (x, y, t). These flows act as kinematic fast dynamos and are able to generate a mean magnetic field uniform and constant in the xy-plane but whose direction varies periodically along z with wavenumber k. Using Mean Field Electrodynamics, the generation mechanism can be understood in terms of a k-dependent α-effect, which depends on the magnetic Reynolds number, R m . We calculate this effect for different motions and investigate how its limit as k?→?0 depends on R m and on the properties of the flows such as their spatial structure or correlation time. This work generalises earlier studies based on 2D steady flows to motions with time dependence.  相似文献   

11.
In Kim et al. (Kim, E., Hughes, D.W. and Soward, A.M., “An investigation into high conductivity dynamo action driven by rotating convection”, Geophys. Astrophys. Fluid Dynam. 91, 303–332 ().) we investigated kinematic dynamo action driven by rapidly rotating convection in a cylindrical annulus. Here we extend this work to consider self-consistent nonlinear dynamo action in which the back-reaction of the Lorentz force on the flow is taken into account. In particular, we investigate, as a function of magnetic Prandtl number, the evolution of an initially weak magnetic field in two different types of convective flow – one chaotic and the other integrable. On saturation, the latter shows a systematic dependence on the magnetic Prandtl number whereas the former appears not to. In addition, we show how, in keeping with the findings of Cattaneo et al. (Cattaneo, F., Hughes, D.W. and Kim, E., “Suppression of chaos in a simplified nonlinear dynamo model”, Phys. Rev. Lett. 76, 2057–2060 ().), saturation of the growth of the magnetic field is brought about, for the originally chaotic flow, by a strong suppression of chaos.  相似文献   

12.
Abstract

The kinematic dynamo problem is considered for certain steady velocity fields with symmetries that are plausible in a rapidly rotating convective system. By generalizing results proved for the mean field dynamo model by Proctor (1977a), it is shown that for a related “comparison problem” with modified boundary conditions, the eigenvalues are degenerate if there is no axisymmetric mean circulation, with modes of dipole and quadrupole parity excited with equal ease. The comparison problem can be shown to be closely similar to the dynamo problem when there is a region unfavourable to dynamo action surrounding the dynamo region. The near-symmetries found by Roberts (1972) for the mean field model are invoked to suggest that a close correspondence is likely even when this region is absent. It is therefore conjectured that such mean motions may be important in explaining the observed preference for solutions of dipole parity by planetary dynamos.  相似文献   

13.
In an electrically conducting fluid, two types of turbulence with a preferred direction are distinguished: planar turbulence, in which every velocity in the turbulent ensemble of flows has no component in the given direction; and two-dimensional turbulence, in which every velocity in the turbulent ensemble is invariant under translation in the preferred direction. Under the additional assumptions of two-scale and homogeneous turbulence with zero mean flow, the associated magnetohydrodynamic alpha- and beta-effects are derived in the second-order correlation approximation (SOCA) when the electrically conducting fluid occupies all space. Limitations of the SOCA are well known, but alpha- and beta-effects of a turbulent flow are useful in interpreting the dynamo effects of the turbulence. Two antidynamo theorems, which establish necessary conditions for dynamo action, are shown to follow from the special structures of these alpha- and beta-effects. The theorems, which are analogues of the laminar planar velocity and two-dimensional antidynamo theorems, apply to all turbulent ensembles with the prescribed alpha- and beta-effects, not just the planar and two-dimensional ensembles. The mean magnetic field is general in the planar theorem but only two-dimensional in the two-dimensional theorem. The two theorems relax the previous restriction to turbulence which is both two-dimensional and planar. The laminar theorems imply decay of the total magnetic field for any velocity of the associated turbulent ensemble. However, the mean-field theorems are not fully consistent with the laminar theorems because further conditions beyond those arising from the turbulence must be imposed on the beta-effect to establish decay of the mean magnetic field. In particular, negative turbulent magnetic diffusivities must be restricted. It is interesting that there is no inconsistency in the alpha-effects. The failure of the SOCA with the two-scale approximation to simply preserve the laminar antidynamo theorems at the beta-effect level is a further demonstration of the restricted validity of the theory and shows that negative diffusivity effects derived by approximation methods must be treated cautiously.  相似文献   

14.
Abstract

The asymptotic and the no-z approximation methods of solving the axisymmetric mean field αΩ dynamo equation in a galactic disc are compared. The behaviour of the solutions is explored in both the linear and nonlinear regimes for a variety of dynamo parameters and two different rotation curves. The solutions obtained from the two different approaches are found to be in good agreement.  相似文献   

15.
We discuss the effects of galactic spiral arms on the -coefficient, turbulent diffusivity and turbulent energy density of the interstellar turbulence. We argue that the -coefficient and the dynamo number are larger in the interarm regions, whereas the kinetic energy density of turbulence is larger in the arms; the turbulent magnetic diffusivity can be only weakly affected by the spiral pattern.  相似文献   

16.
Abstract

In order to show that aperiodic magnetic cycles, with Maunder minima, can occur naturally in nonlinear hydromagnetic dynamos, we have investigated a simple nonlinear model of an oscillatory stellar dynamo. The parametrized mean field equations in plane geometry have a Hopf bifurcation when the dynamo number D=1, leading to Parker's dynamo waves. Including the nonlinear interaction between the magnetic field and the velocity shear results in a system of seven coupled nonlinear differential equations. For D>1 there is an exact nonlinear solution, corresponding to periodic dynamo waves. In the regime described by a fifth order system of equations this solution remains stable for all D and the velocity shear is progressively reduced by the Lorentz force. In a regime described by a sixth order system, the solution becomes unstable and successive transitions lead to chaotic behaviour. Oscillations are aperiodic and modulated to give episodes of reduced activity.  相似文献   

17.
ABSTRACT

Magnetic fields of planets, stars and galaxies are generated by self-excitation in moving electrically conducting fluids. Once produced, magnetic fields can play an active role in cosmic structure formation by destabilising rotational flows that would be otherwise hydrodynamically stable. For a long time, both hydromagnetic dynamo action as well as magnetically triggered flow instabilities had been the subject of purely theoretical research. Meanwhile, however, the dynamo effect has been observed in large-scale liquid sodium experiments in Riga, Karlsruhe and Cadarache. In this paper, we summarise the results of liquid metal experiments devoted to the dynamo effect and various magnetic instabilities such as the helical and the azimuthal magnetorotational instability and the Tayler instability. We discuss in detail our plans for a precession-driven dynamo experiment and a large-scale Tayler–Couette experiment using liquid sodium, and on the prospects to observe magnetically triggered instabilities of flows with positive shear.  相似文献   

18.
Abstract

A spherical mean-field dynamo model is considered in which both the mean motion and the mean electro-motive force due to fluctuating motions show some spherical symmetry. It is shown that under some reasonable assumptions the magnetic field is bound to decay to zero.  相似文献   

19.
Abstract

In this paper a method for solving the equation for the mean magnetic energy <BB> of a solar type dynamo with an axisymmetric convection zone geometry is developed and the main features of the method are described. This method is referred to as the finite magnetic energy method since it is based on the idea that the real magnetic field B of the dynamo remains finite only if <BB> remains finite. Ensemble averaging is used, which implies that fields of all spatial scales are included, small-scale as well as large-scale fields. The method yields an energy balance for the mean energy density ε ≡ B 2/8π of the dynamo, from which the relative energy production rates by the different dynamo processes can be inferred. An estimate for the r.m.s. field strength at the surface and at the base of the convection zone can be found by comparing the magnetic energy density and the outgoing flux at the surface with the observed values. We neglect resistive effects and present arguments indicating that this is a fair assumption for the solar convection zone. The model considerations and examples presented indicate that (1) the energy loss at the solar surface is almost instantaneous; (2) the convection in the convection zone takes place in the form of giant cells; (3) the r.m.s. field strength at the base of the solar convection zone is no more than a few hundred gauss; (4) the turbulent diffusion coefficient within the bulk of the convection zone is about 1014cm2s?1, which is an order of magnitude larger than usually adopted in solar mean field models.  相似文献   

20.
There has for many years been interest in finding necessary conditions for dynamo action. These are usually expressed in terms of bounds on integrated properties of the flow. The bounds can clearly be improved when the flow structure can be taken into account. Recent research presents techniques for finding optimised dynamos (that is with the lowest dynamo threshold) subject to constraints, (e.g. with fixed mean square vorticity). It is natural to ask if such an optimum solution can exist when the mean square velocity is fixed. The aim of this note is to show that this is not the case and in fact that a steady or periodic dynamo can exist in a bounded conductor with an arbitrarily small value of the kinetic energy.  相似文献   

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