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1.
A plane‐shear flow in a fluid with forced turbulence is considered. If the fluid is electrically‐conducting then a mean electromotive force (EMF) results even without basic rotation and the magnetic diffusivity becomes a highly anisotropic tensor. It is checked whether in this case self‐excitation of a large‐scale magnetic field is possible (so‐called W̄ × J̄ ‐dynamo) and the answer is NO. The calculations reveal the cross‐stream components of the EMF perpendicular to the mean current having the wrong signs, at least for small magnetic Prandtl numbers. After our results numerical simulations with magnetic Prandtl number of about unity have only a restricted meaning as the Prandtl number dependence of the diffusivity tensor is rather strong. If, on the other hand, the turbulence field is strati.ed in the vertical direction then a dynamo‐active α ‐effect is produced. The critical magnetic Reynolds number for such a self‐excitation in a simple shear flow is slightly above 10 like for the other – but much more complicated – flow patterns used in existing dynamo experiments with liquid sodium or gallium. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

2.
Using simulations of helically driven turbulence, it is shown that the ratio of kinetic to magnetic energy dissipation scales with the magnetic Prandtl number in power law fashion with an exponent of approximately 0.6. Over six orders of magnitude in the magnetic Prandtl number the magnetic field is found tobe sustained by large‐scale dynamo action of alphasquared type. This work extends a similar finding for small magnetic Prandtl numbers to the regime of large magnetic Prandtl numbers. At large magnetic Prandtl numbers, most of the energy is dissipated viscously, lowering thus the amount of magnetic energy dissipation, which means that simulations can be performed at magnetic Reynolds numbers that are large compared to the usual limits imposed by a given resolution. This is analogous to an earlier finding that at small magnetic Prandtl numbers, most of the energy is dissipated resistively, lowering the amount of kinetic energy dissipation, so simulations can then be performed at much larger fluid Reynolds numbers than otherwise. The decrease in magnetic energy dissipation at large magnetic Prandtl numbers is discussed in the context of underluminous accretion found in some quasars (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

3.
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 3π /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. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

4.
Identifying generic physical mechanisms responsible for the generation of magnetic fields and turbulence in differentially rotating flows is fundamental to understand the dynamics of astrophysical objects such as accretion disks and stars. In this paper, we discuss the concept of subcritical dynamo action and its hydrodynamic analogue exemplified by the process of nonlinear transition to turbulence in non‐rotating wall‐bounded shear flows. To illustrate this idea, we describe some recent results on nonlinear hydrodynamic transition to turbulence and nonlinear dynamo action in rotating shear flows pertaining to the problem of turbulent angular momentum transport in accretion disks. We argue that this concept is very generic and should be applicable to many astrophysical problems involving a shear flow and non‐axisymmetric instabilities of shearinduced axisymmetric toroidal velocity or magnetic fields, such as Kelvin‐Helmholtz, magnetorotational, Tayler or global magnetoshear instabilities. In the light of several recent numerical results, we finally suggest that, similarly to a standard linear instability, subcritical MHD dynamo processes in high‐Reynolds number shear flows could act as a large‐scale driving mechanism of turbulent flows that would in turn generate an independent small‐scale dynamo. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

5.
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 (2001, ApJ 550, 752). 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. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

6.
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 α effect, is important for large‐scale dynamos. Only a few examples of the aforementioned first part 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 (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

7.
Turbulent plane‐shear flow is found to show same basic effects of mean‐fieldMHD as rotating turbulence. In particular, the mean electromotive force (EMF) includes highly anisotropic turbulent diffusion and alpha‐effect. Only magnetic diffusion remains for spatially‐uniform turbulence. The question is addressed whether in this case a self‐excitation of a magnetic field by so‐called sher‐current dynamo is possible and the quasilinear theory provides a negative answer. The streamaligned component of the EMF has the sign opposite to that required for dynamo. If, however, the turbulence is not uniform across the flow direction then a dynamo‐active α ‐effect emerges. The critical magnetic Reynolds number for the alpha‐shear dynamo is estimated to be slightly above ten. Possibilities for cross‐checking theoretical predictions with MHD experiments are discussed. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

8.
We show that a steady mean-field dynamo in astrophysical rotators leads to an outflow of relative magnetic helicity and thus magnetic energy available for particle and wind acceleration in a corona. The connection between energy and magnetic helicity arises because mean-field generation is linked to an inverse cascade of magnetic helicity. To maintain a steady state in large magnetic Reynolds number rotators, there must then be an escape of relative magnetic helicity associated with the mean field, accompanied by an equal and opposite contribution from the fluctuating field. From the helicity flow, a lower limit on the magnetic energy deposited in the corona can be estimated. Steady coronal activity including the dissipation of magnetic energy, and formation of multi-scale helical structures therefore necessarily accompanies an internal dynamo. This highlights the importance of boundary conditions which allow this to occur for non-linear astrophysical dynamo simulations. Our theoretical estimate of the power delivered by a mean-field dynamo is consistent with that inferred from observations to be delivered to the solar corona, the Galactic corona, and Seyfert 1 AGN coronae.  相似文献   

9.
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 (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

10.
When scale separation in space or time is poor, the mean‐field α effect and turbulent diffusivity have to be replaced by integral kernels by which the dependence of the mean electromotive force on the mean magnetic field becomes nonlocal. Earlier work in computing these kernels using the test‐field method is now generalized to the case in which both spatial and temporal scale separations are poor. The approximate form of the kernel for isotropic stationary turbulence is such that it can be treated in a straightforward manner by solving a partial differential equation for the mean electromotive force. The resulting mean‐field equations are solved for oscillatory α –shear dynamos as well as α2 dynamos with α linearly depending on position, which makes this dynamo oscillatory, too. In both cases, the critical values of the dynamo number is lowered due to spatio‐temporal nonlocality.When scale separation in space or time is poor, the mean‐field α effect and turbulent diffusivity have to be replaced by integral kernels by which the dependence of the mean electromotive force on the mean magnetic field becomes nonlocal. Earlier work in computing these kernels using the test‐field method is now generalized to the case in which both spatial and temporal scale separations are poor. The approximate form of the kernel for isotropic stationary turbulence is such that it can be treated in a straightforward manner by solving a partial differential equation for the mean electromotive force. The resulting mean‐field equations are solved for oscillatory α –shear dynamos as well as α2 dynamos  相似文献   

11.
We study the evolution of growth and decay laws for the magnetic field coherence length ξ, 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 ξ ∼ t1/2. This in turn implies that magnetic helicity decays as H ∼ t–2s, where s = (ξdiff/ξH)2, in terms of ξdiff, the diffusion length scale, and ξH, a length scale defined from the helicity power spectrum. The relative magnetic helicity remains constant, implying that the magnetic energy decays as EM ∼ t–1/2–2s. The parameter s is inversely proportional to the magnetic Reynolds number ReM, which is constant in the self‐similar regime. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

12.
The components of the total stress tensor (Reynolds stress plus Maxwell stress) are computed within the quasilinear approximation for a driven turbulence influenced by a large‐scale magnetic background field. The conducting fluid has an arbitrary magnetic Prandtl number and the turbulence without the background field is assumed as homogeneous and isotropic with a free Strouhal number St. The total large‐scale magnetic tension is always reduced by the turbulence with the possibility of a ‘catastrophic quenching’ for large magnetic Reynolds number Rm so that even its sign is reversed. The total magnetic pressure is enhanced by turbulence in the high‐conductivity limit but it is reduced in the low‐conductivity limit. Also in this case the sign of the total pressure may reverse but only for special turbulences with sufficiently large St > 1. The turbulence‐induced terms of the stress tensor are suppressed by strong magnetic fields. For the tension term this quenching grows with the square of the Hartmann number of the magnetic field. For microscopic (i.e. small) diffusivity values the magnetic tension term becomes thus highly quenched even for field amplitudes much smaller than their equipartition value. In the opposite case of large‐eddy simulations the magnetic quenching is only mild but then also the turbulence‐induced Maxwell tensor components for weak fields remain rather small (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

13.
The generation of magnetic field in a homogeneous, electrically conducting fluid – as required for the dynamo generation of the fields of many astrophysical bodies – is normally a threshold process; the dynamo mechanism, applicable to such bodies in unmagnetised environments, requires motions of sufficient strength to overcome the innate magnetic diffusion. In the presence of an ambient field, however, the critical nature of the field generation process is relaxed. Motions can distort and amplify the ambient field for all amplitudes of flow. For motions with appropriate geometries, an internal ‘dynamo‐like’ field of appreciable strength can be generated, even for relatively weak flows. At least a minority of planets, moons and other bodies exist within significant external astrophysical fields. For these bodies, the ambient field problem is more relevant than the classical dynamo problem, yet it remains relatively little studied. In this paper we consider the effect of an axial ambient field on a spherical mean‐field α 2ω dynamo model, through nonlinear calculations with α ‐quenching feedback. Ambient fields of varying strengths, and both stationary and oscillatory in time, are imposed. Particular focus is placed on the effects of these fields on the equatorial symmetry and the time dependence of the preferred solutions. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

14.
In the context of astrophysical dynamos we illustrate that the no-cosines flow, with zero mean helicity, can drive fast dynamo action and we study the dynamo’s mode of operation during both the linear and non-linear saturation regimes. It turns out that in addition to a high growth rate in the linear regime, the dynamo saturates at a level significantly higher than normal turbulent dynamos, namely at exact equipartition when the magnetic Prandtl number Prm∼ 1. Visualization of the magnetic and velocity fields at saturation will help us to understand some of the aspects of the non-linear dynamo problem.  相似文献   

15.
A model is presented for an accretion disc with turbulent viscosity and a magnetically influenced wind. The magnetic field is generated by a dynamo in the disc, involving the turbulence and radial shear. Disc-wind solutions are found for which the wind mass flux is sufficient to play a major part in driving an imposed steady inflow, but small enough for most material to be accreted on to the central object. Constraints arise for the magnetic Reynolds and Prandtl numbers in terms of the turbulent Mach number and vertical length-scale of the disc's horizontal magnetic field. It is shown that the imposition of a stellar boundary condition enhances the wind mass flux in the very inner region of the disc and may result in jet formation.  相似文献   

16.
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 α. For solar parameters, typical magnetic helicity fluxes lie around 1047 Mx2 per cycle.  相似文献   

17.
Toroidal magnetic fields subject to the Tayler instability can transport angular momentum. We show that the Maxwell and Reynolds stress of the nonaxisymmetric field pattern depend linearly on the shear in the cylindrical gap geometry. Resulting angular momentum transport also scales linear with shear. It is directed outwards for astrophysical relevant flows and directed inwards for superrotating flows with dΩ/dR > 0. We define an eddy viscosity based on the linear relation between shear and angular momentum transport and show that its maximum for given Prandtl and Hartmann number depends linear on the magnetic Reynolds number Rm. For Rm ≃ 1000 the eddy viscosity is of the size of 30 in units of the microscopic value. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

18.
Future radio observations with the Square Kilometre Array (SKA) and its precursors will be sensitive to trace spiral galaxies and their magnetic field configurations up to redshift z ≈ 3. We suggest an evolutionary model for the magnetic configuration in star‐forming disk galaxies and simulate the magnetic field distribution, the total and polarized synchrotron emission, and the Faraday rotation measures for disk galaxies at z ≲ 3. Since details of dynamo action in young galaxies are quite uncertain, we model the dynamo action heuristically relying only on well‐established ideas of the form and evolution of magnetic fields produced by the mean‐field dynamo in a thin disk. We assume a small‐scale seed field which is then amplified by the small‐scale turbulent dynamo up to energy equipartition with kinetic energy of turbulence. The large‐scale galactic dynamo starts from seed fields of 100 pc and an averaged regular field strength of 0.02 μG, which then evolves to a “spotty” magnetic field configuration in about 0.8 Gyr with scales of about one kpc and an averaged regular field strength of 0.6 μG. The evolution of these magnetic spots is simulated under the influence of star formation, dynamo action, stretching by differential rotation of the disk, and turbulent diffusion. The evolution of the regular magnetic field in a disk of a spiral galaxy, as well as the expected total intensity, linear polarization and Faraday rotation are simulated in the rest frame of a galaxy at 5GHz and 150 MHz and in the rest frame of the observer at 150 MHz. We present the corresponding maps for several epochs after disk formation. Dynamo theory predicts the generation of large‐scale coherent field patterns (“modes”). The timescale of this process is comparable to that of the galaxy age. Many galaxies are expected not to host fully coherent fields at the present epoch, especially those which suffered from major mergers or interactions with other galaxies. A comparison of our predictions with existing observations of spiral galaxies is given and discussed (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

19.
In the theory of homogeneous, stationary, axisymmetric, incompressible velocity turbulence there arise four scalar functions. The incompressibility condition provides two relations between these four functions.We will demonstrate here that application of Cramér's theorem imposes two additional constraints on the four functions. These constraints do not uniquely define the allowed functional form but they do provide very powerful criteria for limiting the class of functions which are permitted. In view of the growing use of velocity turbulence in kinematic dynamo theory and its importance in astrophysical situations (e.g., Earth, Sun, Galaxy) to maintain or regenerate a large scale magnetic field, we believe that the present constraints are of more than academic interest. In particular, application of the constraints to a form of velocity turbulence used by Steenbeck, Krause and Rädler when computing kinematic dynamo action, shows that their assumed turbulence is not physically realizable in nature.  相似文献   

20.
Observations in polarized emission reveal the existence of large‐scale coherent magnetic fields in a wide range of spiral galaxies. Radio‐polarization data show that these fields are strongly inclined towards the radial direction, with pitch angles up to 35° and thus cannot be explained by differential rotation alone. Global dynamo models describe the generation of the radial magnetic field from the underlying turbulence via the so called α ‐effect. However, these global models still rely on crude assumptions about the small‐scale turbulence. To overcome these restrictions we perform fully dynamical MHD simulations of interstellar turbulence driven by supernova explosions. From our simulations we extract profiles of the contributing diagonal elements of the dynamo α ‐tensor as functions of galactic height. We also measure the coefficients describing vertical pumping and find that the ratio between these two effects has been overestimated in earlier analytical work, where dynamo action seemed impossible. In contradiction to these models based on isolated remnants we always find the pumping to be directed inward. In addition we observe that depends on whether clustering in terms of superbubbles is taken into account. Finally, we apply a test field method to derive a quantitative measure of the turbulent magnetic diffusivity which we determine to be ∼2 kpckms–1. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

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