New mechanism of generation of large-scale magnetic field in a sheared turbulent plasma

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 effect. However, there is no dynamo action due to the shear-current effect for small hydrodynamic and magnetic Reynolds numbers even in a turbulent convection, if the spatial scaling for the turbulent correlation time is k^{-2}, where k is the small-scale wave number. We discuss here also the nonlinear mean-field dynamo due to the shear-current effect and take into account the transport of magnetic helicity as a dynamical nonlinearity. The magnetic helicity flux strongly affects the magnetic field dynamics in the nonlinear stage of the dynamo action. When the magnetic helicity flux is not small, the saturated level of the mean magnetic field is of the order of the equipartition field determined by the turbulent kinetic energy. The obtained results are important for elucidation of origin of the large-scale magnetic fields in astrophysical and cosmic sheared turbulent plasma.Comment: 7 pages, Planetory and Space Science, in pres

Mean-field theory of differential rotation in density stratified turbulent convection

A mean-field theory of differential rotation in a density stratified turbulent convection has been developed. This theory is based on a combined effect of the turbulent heat flux and anisotropy of turbulent convection on the Reynolds stress. A coupled system of dynamical budget equations consisting in the equations for the Reynolds stress, the entropy fluctuations and the turbulent heat flux has been solved. To close the system of these equations, the spectral tau approach which is valid for large Reynolds and Peclet numbers, has been applied. The adopted model of the background turbulent convection takes into account an increase of the turbulence anisotropy and a decrease of the turbulent correlation time with the rotation rate. This theory yields the radial profile of the differential rotation which is in agreement with that for the solar differential rotation.Comment: 13 pages, 5 figures, jpp.cls, revised. arXiv admin note: text overlap with arXiv:astro-ph/060254

Compressibility in turbulent MHD and passive scalar transport: mean-field theory

We develop a mean-field theory of compressibility effects in turbulent magnetohydrodynamics and passive scalar transport using the quasi-linear approximation and the spectral $\tau$-approach. We find that compressibility decreases the $\alpha$ effect and the turbulent magnetic diffusivity both at small and large magnetic Reynolds numbers, Rm. Similarly, compressibility decreases the turbulent diffusivity for passive scalars both at small and large P\'eclet numbers, Pe. On the other hand, compressibility does not affect the effective pumping velocity of the magnetic field for large Rm, but it decreases it for small Rm. Density stratification causes turbulent pumping of passive scalars, but it is found to become weaker with increasing compressibility. No such pumping effect exists for magnetic fields. However, compressibility results in a new passive scalar pumping effect from regions of low to high turbulent intensity both for small and large P\'eclet numbers. It can be interpreted as compressible turbophoresis of noninertial particles and gaseous admixtures, while the classical turbophoresis effect exists only for inertial particles and causes them to be pumped to regions with lower turbulent intensity.Comment: 26 pages, 1 figure, final paper accepted for publication to JPP, jpp.cl

The shear dynamo problem for small magnetic Reynolds numbers

We study large-scale dynamo action due to turbulence in the presence of a linear shear flow, in the low conductivity limit. Our treatment is nonperturbative in the shear strength and makes systematic use of both the shearing coordinate transformation and the Galilean invariance of the linear shear flow. The velocity fluctuations are assumed to have low magnetic Reynolds number (Rm) but could have arbitrary fluid Reynolds number. The magnetic fluctuations are determined to lowest order in Rm by explicit calculation of the resistive Green's function for the linear shear flow. The mean electromotive force is calculated and an integro-differential equation is derived for the time evolution of the mean magnetic field. In this equation, velocity fluctuations contribute to two different kinds of terms, the C and D terms, in which first and second spatial derivatives of the mean magnetic field, respectively, appear inside the spacetime integrals. The contribution of the D terms is such that the time evolution of the cross-shear components of the mean field do not depend on any other components excepting themselves. Therefore, to lowest order in Rm but to all orders in the shear strength, the D terms cannot give rise to a shear-current assisted dynamo effect. Casting the integro-differential equation in Fourier space, we show that the normal modes of the theory are a set of shearing waves, labelled by their sheared wavevectors. The integral kernels are expressed in terms of the velocity spectrum tensor, which is the fundamental quantity that needs to be specified to complete the integro-differential equation description of the time evolution of the mean magnetic field.Comment: Near-final version; Accepted for publication in the Journal of Fluid Mechanics; References added; 22 pages, 2 figure

Turbulent fluxes of entropy and internal energy in temperature stratified flows

We derive equations for the mean entropy and the mean internal energy in the low-Mach-number temperature stratified turbulence (i.e., for turbulent convection or stably stratified turbulence), and show that turbulent flux of entropy is given by ${\bf F}_s=\overline{\rho} \, \overline{{\bf u} s}$, where $\overline{\rho}$ is the mean fluid density, $s$ are fluctuations of entropy and overbars denote averaging over an ensemble of turbulent velocity field, ${\bf u}$. We demonstrate that the turbulent flux of entropy is different from the turbulent convective flux, ${\bf F}_c=\overline{T} \, \overline{\rho} \, \overline{{\bf u} s}$, of the fluid internal energy, where $\overline{T}$ is the mean fluid temperature. This turbulent convective flux is well-known in the astrophysical and geophysical literature, and it cannot be used as a turbulent flux in the equation for the mean entropy. This result is exact for low-Mach-number temperature stratified turbulence and is independent of the model used. We also derive equations for the velocity-entropy correlation, $\overline{{\bf u} s}$, in the limits of small and large Peclet numbers, using the quasi-linear approach and the spectral tau approximation, respectively. This study is important in view of different applications to the astrophysical and geophysical temperature stratified turbulence.Comment: 10 pages, Journal of Plasma Physics, 2015, in pres

Enhancement of small-scale turbulent dynamo by large-scale shear

Small-scale dynamos are ubiquitous in a broad range of turbulent flows with large-scale shear, ranging from solar and galactic magnetism to accretion disks, cosmology and structure formation. Using high-resolution direct numerical simulations we show that in non-helically forced turbulence with zero mean magnetic field, large-scale shear supports small-scale dynamo action, i.e., the dynamo growth rate increases with shear and shear enhances or even produces turbulence, which, in turn, further increases the dynamo growth rate. When the production rates of turbulent kinetic energy due to shear and forcing are comparable, we find scalings for the growth rate $\gamma$ of the small-scale dynamo and the turbulent velocity $u_{\rm rms}$ with shear rate $S$ that are independent of the magnetic Prandtl number: $\gamma \propto |S|$ and $u_{\rm rms} \propto |S|^{2/3}$. For large fluid and magnetic Reynolds numbers, $\gamma$, normalized by its shear-free value, depends only on shear. Having compensated for shear-induced effects on turbulent velocity, we find that the normalized growth rate of the small-scale dynamo exhibits the scaling, $\widetilde{\gamma}\propto |S|^{2/3}$, arising solely from the induction equation for a given velocity field.Comment: Improved version submitted to the Astrophysical Journal Letters, 6 pages, 5 figure

The negative effective magnetic pressure in stratified forced turbulence

To understand the basic mechanism of the formation of magnetic flux concentrations, we determine by direct numerical simulations the turbulence contributions to the mean magnetic pressure in a strongly stratified isothermal layer with large plasma beta, where a weak uniform horizontal mean magnetic field is applied. The negative contribution of turbulence to the effective mean magnetic pressure is determined for strongly stratified forced turbulence over a range of values of magnetic Reynolds and Prandtl numbers. Small-scale dynamo action is shown to reduce the negative effect of turbulence on the effective mean magnetic pressure. However, the turbulence coefficients describing the negative effective magnetic pressure phenomenon are found to be converged for magnetic Reynolds numbers between 60 and 600, which is the largest value considered here. In all these models the turbulent intensity is arranged to be nearly independent of height, so the kinetic energy density decreases with height due to the decrease in density. In a second series of numerical experiments, the turbulent intensity increases with height such that the turbulent kinetic energy density is nearly independent of height. Turbulent magnetic diffusivity and turbulent pumping velocity are determined with the test-field method for both cases. The vertical profile of the turbulent magnetic diffusivity is found to agree with what is expected based on simple mixing length expressions. Turbulent pumping is shown to be down the gradient of turbulent magnetic diffusivity, but it is twice as large as expected. Corresponding numerical mean-field models are used to show that a large-scale instability can occur in both cases, provided the degree of scale separation is large enough and hence the turbulent magnetic diffusivity small enough.Comment: 15 pages, 18 figures, 2 tables, ApJ, accepte