Numerical simulations of forced turbulence in elongated shearing boxes are carried out to demonstrate that a nonhelical turbulence in conjunction with a linear shear can give rise to a mean-field dynamo. Exponential growth of magnetic field at scales larger than the outer (forcing) scale of the turbulence is found. Over a range of values of the shearing rate S spanning approximately two orders of magnitude, the growth rate of the magnetic field is proportional to the imposed shear, gamma ~ S, while the characteristic spatial scale of the field is l_b ~ S^(-1/2). The effect is quite general: earlier results for the nonrotating case by Yousef et al. 2008 (PRL 100, 184501) are extended to shearing boxes with Keplerian rotation; it is also shown that the shear dynamo mechanism operates both below and above the threshold for the fluctuation dynamo. The apparently generic nature of the shear dynamo effect makes it an attractive object of study for the purpose of understanding the generation of magnetic fields in astrophysical systems.
Mechanisms of nonhelical large-scale dynamos (shear-current dynamo and effect of homogeneous kinetic helicity fluctuations with zero mean) in a homogeneous turbulence with large-scale shear are discussed. We have found that the shear-current dynamo can act even in random flows with small Reynolds numbers. However, in this case mean-field dynamo requires small magnetic Prandtl numbers (i.e., ${\rm Pm} < {\rm Pm}^{\rm cr}<1$). The threshold in the magnetic Prandtl number, ${\rm Pm}^{\rm cr} = 0.24$, is determined using second order correlation approximation (or first-order smoothing approximatio…
The nonlinear mean-field dynamo due to a shear-current effect in a nonhelical homogeneous turbulence with a mean velocity shear is discussed. The transport of magnetic helicity as a dynamical nonlinearity is taken into account. The shear-current effect is associated with the ${\bf W} {\bf \times} {\bf J}$ term in the mean electromotive force, where ${\bf W}$ is the mean vorticity due to the large-scale shear motions and ${\bf J}$ is the mean electric current. This effect causes the generation of large-scale magnetic field in a turbulence with large hydrodynamic and magnetic Reynolds numbers. T…
The effect of shear on the growth of large scale magnetic fields in helical turbulence is investigated. The resulting large-scale magnetic field is also helical and continues to evolve, after saturation of the small scale field, on a slow resistive time scale. This is a consequence of magnetic helicity conservation. Because of shear, the time scale needed to reach an equipartition-strength large scale field is shortened proportionally to the ratio of the resulting toroidal to poloidal large scale fields.
A review of recent studies on a new mechanism of generation of large-scale magnetic field in a sheared turbulent plasma is presented. This mechanism is associated with the shear-current effect which is related to the W x J-term in the mean electromotive force. This effect causes the generation of the large-scale magnetic field even in a nonrotating and nonhelical homogeneous sheared turbulent convection whereby the alpha effect vanishes. It is found that turbulent convection promotes the shear-current dynamo instability, i.e., the heat flux causes positive contribution to the shear-current eff…
We study effects of kinetic helicity fluctuations in a turbulence with large-scale shear using two different approaches: the spectral tau-approximation and the second order correlation approximation (or first-order smoothing approximation). These two approaches demonstrate that homogeneous kinetic helicity fluctuations alone with zero mean value in a sheared homogeneous turbulence cannot cause large-scale dynamo. Mean-field dynamo can be possible when kinetic helicity fluctuations are inhomogeneous which cause a nonzero mean alpha effect in a sheared turbulence. On the other hand, shear-curren…
We investigate the growth and structure of magnetic fields amplified by kinematic dynamo action in turbulence with non-zero kinetic helicity. We assume a simple Gaussian velocity correlation tensor, which allows us to consider very large magnetic Reynolds numbers, up to one trillion. We use the kinematic Kazantsev-Kraichnan model of dynamo and find a complete numerical solution for the correlation functions of growing magnetic fields.
Helical turbulence is thought to provide the key to the generation of large-scale magnetic fields. Turbulence also generically leads to rapidly growing small-scale magnetic fields correlated on the turbulence scales. These two processes are usually studied separately. We give here a unified treatment of both processes, in the case of random fields, incorporating also a simple model non-linear drift. In the process we uncover an interesting plausible saturated state of the small-scale dynamo and a novel analogy between quantum mechanical (QM) tunneling and the generation of large scale fields. …
Supernovae are the dominant energy source for driving turbulence within the interstellar plasma. Until recently, their effects on magnetic field amplification in disk galaxies remained a matter of speculation. By means of self-consistent simulations of supernova-driven turbulence, we find an exponential amplification of the mean magnetic field on timescales of a few hundred million years. The robustness of the observed fast dynamo is checked at different magnetic Reynolds numbers, and we find sustained dynamo action at moderate Rm. This indicates that the mechanism might indeed be of relevance…
Direct numerical simulations of turbulent Hall dynamos are presented. The evolution of an initially weak and small scale magnetic field in a system maintained in a stationary turbulent regime by a stirring force at a macroscopic scale is studied to explore the conditions for exponential growth of the magnetic energy. Scaling of the dynamo efficiency with the Reynolds numbers is studied, and the resulting total energy spectra are found to be compatible with a Kolmogorov type law. A faster growth of large scale magnetic fields is observed at intermediate intensities of the Hall effect.
We consider the problem of incompressible, forced, nonhelical, homogeneous, isotropic MHD turbulence with no mean magnetic field. This problem is essentially different from the case with externally imposed uniform mean field. There is no scale-by-scale equipartition between magnetic and kinetic energies as would be the case for the Alfven-wave turbulence. The isotropic MHD turbulence is the end state of the turbulent dynamo which generates folded fields with small-scale direction reversals. We propose that the statistics seen in numerical simulations of isotropic MHD turbulence could be explai…
We study a large-scale instability in a sheared nonhelical turbulence that causes generation of large-scale vorticity. Three types of the background large-scale flows are considered, i.e., the Couette and Poiseuille flows in a small-scale homogeneous turbulence, and the "log-linear" velocity shear in an inhomogeneous turbulence. It is known that laminar plane Couette flow and antisymmetric mode of laminar plane Poiseuille flow are stable with respect to small perturbations for any Reynolds numbers. We demonstrate that in a small-scale turbulence under certain conditions the large-scale Couette…
We argue that the recently reported Kolmogorov-like magnetic turbulence spectrum in the cool core of the Hydra A galaxy cluster can be understood by kinetic energy injection by active galaxies that drives a turbulent non-helical magnetic dynamo into its saturated state. Although dramatic differences exist between small-scale dynamo scenarios, their saturated state is expected to be similar, as we show for three scenarios: the flux rope dynamo, the fluctuation dynamo, and the explosive dynamo. Based on those scenarios, we develop an analytical model of the hydrodynamic and magnetic turbulence i…
The nonlinear coefficients defining the mean electromotive force (i.e., the nonlinear turbulent magnetic diffusion, the nonlinear effective velocity, the nonlinear kappa-tensor, etc.) are calculated for an anisotropic turbulence. A particular case of an anisotropic background turbulence (i.e., the turbulence with zero mean magnetic field) with one preferential direction is considered. It is shown that the toroidal and poloidal magnetic fields have different nonlinear turbulent magnetic diffusion coefficients. It is demonstrated that even for a homogeneous turbulence there is a nonlinear effect…
We generalize the derivation of dynamo coefficient $α$ of Field et al (1999) to include the following two aspects: first, the de-correlation times of velocity field and magnetic field are different; second, the magnetic Prandtl number can be arbitrary. We find that the contributions of velocity field and magnetic field to the $α$ effect are not equal, but affected by their different statistical properties. In the limit of large kinetic Reynolds number and large magnetic Reynolds number, $α$-coefficient may not be small if the de-correlation times of velocity field and magnetic field are shorte…
(abridged) MHD turbulence is known to exist in shearing boxes with either zero or nonzero net magnetic flux. However, the way turbulence survives in the zero-net-flux case is not explained by linear theory and appears as a purely numerical result. Aims: We look for a nonlinear mechanism able to explain the persistence of MHD turbulence in shearing boxes with zero net magnetic flux, and potentially leading to large-scale dynamo action. Method: Spectral nonlinear simulations of the magnetorotational instability are shown to exhibit a large-scale axisymmetric magnetic field, maintained for a few …
A generalized mean magnetic field induction equation for differential rotators is derived, including a compressibility, and the anisotropy induced on the turbulent quantities from the mean magnetic field itself and a mean velocity shear. Derivations of the mean field equations often do not emphasize that there must be anisotropy and inhomogeneity in the turbulence for mean field growth. The anisotropy from shear is the source of a term involving the product of the mean velocity gradient and the cross-helicity correlation of the isotropic parts of the fluctuating velocity and magnetic field, $\…
Turbulence with a large magnetic Reyonolds number, generically leads to rapidly growing magnetic noise over and above any mean field. We revisit the dynamics of this fluctuating field, in homogeneous, isotropic, helical turbulence. Assuming the turbulence to be Markovian, we first rederive, in a fairly transparent manner, the equation for the mean field, and corrected Fokker-Plank type equations for the magnetic correlations. In these equations, we also incorporate the effects of ambipolar drift which would obtain if the turbulent medium has a significant neutral component. We apply these equa…
The possibility of fast dynamo action by collisionless kinetic Alfven Wave turbulence is demonstrated. The irreversibility necessary to lock in the generated field is provided by electron Landau damping, so the induced electric field does not vanish with resistivity. Mechanisms for self-regulation of the system and the relation of these results to the theory of alpha quenching are discussed. The dynamo-generated fields have symmetry like to that of zonal flows, and thus are termed zonal fields.
This is a brief review of the main results of our recent studies of the nonlinear evolution of the small-scale MHD dynamo in the high-Prandtl-number regime and of the structure of the resulting saturated state of the isotropic homogeneous MHD turbulence. It is emphasized that the MHD regime without a uniform mean field (as is the case in our studies) is fundamentally different from the one in which such a field is externally imposed. The ability of the turbulence to bend and fold the magnetic-field lines leads to the emergence of a distinctive small-scale structure. The fields are organized in…
Dynamical studies of MHD turbulence on the one hand, and arguments based upon magnetic helicity on the other, have yielded seemingly contradictory estimates for the $α$ parameter in turbulent dynamo theory. Here we show, with direct numerical simulation of three-dimensional magnetohydrodynamic turbulence with a mean magnetic field, $\OB$, that the constraint on the dynamo $α$-effect set by the magnetic helicity is time-dependent. A time-scale $t_c$ is introduced such that for $t<t_c$, the $α$-coefficient calculated from the simulation is close to the result of Pouquet et al and Field et al, $-…
Generation of magnetic field energy, without mean field generation, is studied. Isotropic mirror-symmetric turbulence of a conducting fluid amplifies the energy of small-scale magnetic perturbations if the magnetic Reynolds number is high, and the dimensionality of space d satisfies 2.103 < d <8.765. The result does not depend on the model of turbulence, incompressibility and isotropy being the only requirements.
Large-scale magnetic fields in galaxies are thought to be generated by a turbulent dynamo. However the same turbulence also leads to a small-scale dynamo which generates magnetic noise at a more rapid rate. The efficiency of the large-scale dynamo depends on how this noise saturates. We examine this issue taking into account ambipolar drift, which obtains in a galaxy with significant neutral gas. We argue that, (1) the small-scale dynamo generated field does not fill the volume, but is concentrated into intermittent rope like structures. The flux ropes are curved on the turbulent eddy scales. …
Large-scale dynamo action due to turbulence in the presence of a linear shear flow is studied. Our treatment is quasilinear and kinematic but is non perturbative in the shear strength. We derive the integro-differential equation for the evolution of the mean magnetic field, by systematic use of the shearing coordinate transformation and the Galilean invariance of the linear shear flow. For non helical turbulence the time evolution of the cross-shear components of the mean field do not depend on any other components excepting themselves. This is valid for any Galilean-invariant velocity field, …
Magnetically mediated disk outflows are a leading paradigm to explain winds and jets in a variety of astrophysical sources, but where do the fields come from? Since accretion of mean magnetic flux may be disfavored in a thin turbulent disk, and only fields generated with sufficiently large scale can escape before being shredded by turbulence, in situ field production is desirable. Nonlinear helical inverse dynamo theory can provide the desired fields for coronae and outflows. We discuss the implications for contemporary protostellar disks, where the MRI (magneto-rotational instability) can dri…
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 di…
We use direct and stochastic numerical simulations of the magnetohydrodynamic equations to explore the influence of turbulence on the dynamo threshold. In the spirit of the Kraichnan-Kazantsev model, we model the turbulence by a noise, with given amplitude, injection scale and correlation time. The addition of a stochastic noise to the mean velocity significantly alters the dynamo threshold. When the noise is at small (resp. large) scale, the dynamo threshold is decreased (resp. increased). For a large scale noise, a finite correlation time reinforces this effect.
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 fl…
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 larg…
We simulate the evolution of an initially weak magnetic field in forced turbulence for a range of Prandtl numbers. The field grows exponentially with the Kulsrud-Anderson $k^{3/2}$ spectrum until the magnetic energy approaches the viscous-scale kinetic energy, where the magnetic forces then backreact on the velocity. Further growth proceeds more slowly until a saturated state is reached where the magnetic and kinetic energies are equal, and where the magnetic energy exists primarily at the resistive scale. We discuss the structure of this turbulence and the extrapolation of the results to astr…
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 $35\degr$ 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 fu…
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 modelled in terms of an αΩdynamo. 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 α-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 he…
A rigorous theory for the generation of a large-scale magnetic field by random non-helically forced motions of a conducting fluid combined with a linear shear is presented in the analytically tractable limit of low Rm and weak shear. The dynamo is kinematic and due to fluctuations in the net (volume-averaged) electromotive force. This is a minimal proof-of-concept quasilinear calculation aiming to put the shear dynamo, a new effect recently found in numerical experiments, on a firm theoretical footing. Numerically observed scalings of the wavenumber and growth rate of the fastest growing mode,…
It is shown that protostrange stars (PSSs) can be convective and that there are two possible scenarios describing their turbulence. Besides the local turbulence on the scale which is less than the mean free path of neutrinos, large-scale (~1 km) convection also may occur with properties that are similar to those of convection in protoneutron stars (PNSs). We thus suggest that strange stars can also create dynamo-originated magnetic fields during the deleptonization episode soon after a supernova explosion. Further detailed investigations are needed to see whether or not strange stars and neutr…
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 helicit…
We use the mean-field dynamo equations to show that an incoherent alpha effect 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. In accretion disks, this process can lead to axisymmetric magnetic domains whose radial and vertical dimensions will be comparable to the disk height. This process may be responsible for observations of dynamo activity seen in simulations of dynamo-generated turbulence involving, for example, the Balbus-Hawley instability. In this case the magnetic…
Planetary and stellar dynamos likely result from turbulent motions in magnetofluids with kinematic viscosities that are small compared to their magnetic diffusivities. Laboratory experiments are in progress to produce similar dynamos in liquid metals. This work reviews recent computations of thresholds in critical magnetic Reynolds number above which dynamo amplification can be expected for mechanically-forced turbulence (helical and non-helical, short wavelength and long wavelength) as a function of the magnetic Prandtl number $P_M$. New results for helical forcing are discussed, for which a …
It is shown that the turbulent dynamo $α$-effect converts magnetic helicity from the turbulent field to the mean field when the turbulence is electromagnetic while the magnetic helicity of the mean-field is transported across space when the turbulence is electrostatic or due to the electron diamagnetic effect. In all cases, however, the dynamo effect strictly conserves the total helicity except for resistive effects and a small battery effect. Implications for astrophysical situations, especially for the solar dynamo, are discussed.
With a non local shell model of magnetohydrodynamic turbulence we investigate numerically the turbulent dynamo action for low and high magnetic Prandtl numbers ($Pm$). The results obtained in the kinematic regime and along the way to dynamo saturation are understood in terms of a phenomenological approach based on the local ($Pm\ll 1$) or non local ($Pm\gg 1$) nature of the energy transfers. In both cases the magnetic energy grows at small scale and saturates as an inverse `` cascade ''.
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 WxJ-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 m…
The paper deals with a simple spherical mean-field dynamo model of $α^2$-type in the case of high electrical conductivity. A spherically symmetric distribution of turbulent motions is assumed inside a spherical fluid body surrounded by free space, and some complete form of the corresponding mean electromotive force is taken into account. For a turbulence lacking reflectional symmetry finite growth rates of magnetic fields prove to be possible even in the limit of perfect conductivity, that is, the model corresponds to a fast dynamo. In accordance with the theorem by Bondi and Gold the dynamo-g…
We study the magneto-rotational instability of an incompressible flow which rotates with angular velocity Omega(r)=a+b/r^2 where r is the radius and $a$ and b are constants. We find that an applied magnetic field destabilises the flow, in agreement with the results of Rudiger & Zhang 2001. We extend the investigation in the region of parameter space which is Rayleigh stable. We also study the instability at values of magnetic Prandtl number which are much larger and smaller than Rudiger & Zhang. Large magnetic Prandtl numbers are motivated by their possible relevance in the central region of g…
Supernovae are known to be the dominant energy source for driving turbulence in the interstellar medium. Yet, their effect on magnetic field amplification in spiral galaxies is still poorly understood. Previous analytical models, based on the evolution of isolated, non-interacting supernova remnants, predicted a dominant vertical pumping that would render dynamo action improbable. In the present work, we address the issue of vertical transport, which is thought to be the key process that inhibits dynamo action in the galactic context. We aim to demonstrate that supernova driving is a powerful …
The prevailing theory for the origin of cosmic magnetic fields is that they have been amplified to their present values by the turbulent dynamo inductive action in the protogalactic and galactic medium. Up to now, in calculation of the turbulent dynamo, it has been customary to assume that there is no back reaction of the magnetic field on the turbulence, as long as the magnetic energy is less than the turbulent kinetic energy. This assumption leads to the kinematic dynamo theory. However, the applicability of this theory to protogalaxies is rather limited. The reason is that in protogalaxies …
We investigate the structure of magnetic field amplified by turbulent velocity fluctuations, in the framework of the kinematic Kazantsev-Kraichnan model. We consider Kolmogorov distribution of velocity fluctuations, and assume that both Reynolds number and magnetic Reynolds number are very large. We present the full numerical solution of the model for the spectra and the growth rates of magnetic fluctuations. We consider astrophysically relevant limits of large and small magnetic Prandtl numbers, and address both helical and nonhelical cases.
We investigate magnetic field amplification in a turbulent velocity field with nonzero helicity, in the framework of the kinematic Kazantsev-Kraichnan model. We present the numerical solution of the model for the practically important case of Kolmogorov distribution of velocity fluctuations, with a large magnetic Reynolds number. We find that in contrast to the nonhelical case where growing magnetic fields are described by a few bound eigenmodes concentrated inside the inertial interval of the velocity field, in the helical case the number of bound eigenmodes considerably increases; moreover, …
The feasibility of a mean-field dynamo in nonhelical turbulence with superimposed linear shear is studied numerically in elongated shearing boxes. Exponential growth of magnetic field at scales much larger than the outer scale of the turbulence is found. The charateristic scale of the field is l_B ~ S^{-1/2} and growth rate is gamma ~ S, where S is the shearing rate. This newly discovered shear dynamo effect potentially represents a very generic mechanism for generating large-scale magnetic fields in a broad class of astrophysical systems with spatially coherent mean flows.
