Shear-current effect in a turbulent convection with a large-scale shear

The shear-current effect in a nonrotating homogeneous turbulent convection with a large-scale constant shear is studied. The large-scale velocity shear causes anisotropy of turbulent convection, which produces the mean electromotive force \bec{\cal E}^{(W)} \propto {\bf W} {\bf \times} {\bf J} and the mean electric current along the original mean magnetic field, where ${\bf W}$ is the background mean vorticity due to the shear and ${\bf J}$ is the mean electric current. This results in a large-scale dynamo 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 $\tau(k) \propto k^{-2}$, where $k$ is the small-scale wave number.Comment: 8 pages, Physical Review E, in pres

The negative magnetic pressure effect in stratified turbulence

While the rising flux tube paradigm is an elegant theory, its basic assumptions, thin flux tubes at the bottom of the convection zone with field strengths two orders of magnitude above equipartition, remain numerically unverified at best. As such, in recent years the idea of a formation of sunspots near the top of the convection zone has generated some interest. The presence of turbulence can strongly enhance diffusive transport mechanisms, leading to an effective transport coefficient formalism in the mean-field formulation. The question is what happens to these coefficients when the turbulence becomes anisotropic due to a strong large-scale mean magnetic field. It has been noted in the past that this anisotropy can also lead to highly non-diffusive behaviour. In the present work we investigate the formation of large-scale magnetic structures as a result of a negative contribution of turbulence to the large-scale effective magnetic pressure in the presence of stratification. In direct numerical simulations of forced turbulence in a stratified box, we verify the existence of this effect. This phenomenon can cause formation of large-scale magnetic structures even from initially uniform large-scale magnetic field.Comment: 5 pages, 2 figures, submitted conference proceedings IAU symposium 273 "Physics of Sun and Star Spots

The dynamics of Wolf numbers based on nonlinear dynamo with magnetic helicity: comparisons with observations

We investigate the dynamics of solar activity using a nonlinear one-dimensional dynamo model and a phenomenological equation for the evolution of Wolf numbers. This system of equations is solved numerically. We take into account the algebraic and dynamic nonlinearities of the alpha effect. The dynamic nonlinearity is related to the evolution of a small-scale magnetic helicity, and it leads to a complicated behavior of solar activity. The evolution equation for the Wolf number is based on a mechanism of formation of magnetic spots as a result of the negative effective magnetic pressure instability (NEMPI). This phenomenon was predicted 25 years ago and has been investigated intensively in recent years through direct numerical simulations and mean-field simulations. The evolution equation for the Wolf number includes the production and decay of sunspots. Comparison between the results of numerical simulations and observational data of Wolf numbers shows a 70 % correlation over all intervals of observation (about 270 years). We determine the dependence of the maximum value of the Wolf number versus the period of the cycle and the asymmetry of the solar cycles versus the amplitude of the cycle. These dependencies are in good agreement with observations.Comment: 9 pages, 13 figures, final revised paper for MNRA

Nonlinear Turbulent Magnetic Diffusion and Mean-Field Dynamo

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 effective velocity which exhibits diamagnetic or paramagnetic properties depending on anisotropy of turbulence and level of magnetic fluctuations in the background turbulence. Analysis shows that an anisotropy of turbulence strongly affects the nonlinear mean electromotive force. Two types of nonlinearities (algebraic and dynamic) are also discussed. The algebraic nonlinearity implies a nonlinear dependence of the mean electromotive force on the mean magnetic field. The dynamic nonlinearity is determined by a differential equation for the magnetic part of the alpha-effect. It is shown that for the alpha-Omega axisymmetric dynamo the algebraic nonlinearity alone cannot saturate the dynamo generated mean magnetic field while the combined effect of the algebraic and dynamic nonlinearities limits the mean magnetic field growth. Astrophysical applications of the obtained results are discussed.Comment: 15 pages, REVTEX

Nonlinear turbulent magnetic diffusion and effective drift velocity of large-scale magnetic field in a two-dimensional magnetohydrodynamic turbulence

We study a nonlinear quenching of turbulent magnetic diffusion and effective drift velocity of large-scale magnetic field in a developed two-dimensional MHD turbulence at large magnetic Reynolds numbers. We show that transport of the mean-square magnetic potential strongly changes quenching of turbulent magnetic diffusion. In particularly, the catastrophic quenching of turbulent magnetic diffusion does not occur for the large-scale magnetic fields $B \gg B_{\rm eq} / \sqrt{\rm Rm}$ when a divergence of the flux of the mean-square magnetic potential is not zero, where $B_{\rm eq}$ is the equipartition mean magnetic field determined by the turbulent kinetic energy and Rm is the magnetic Reynolds number. In this case the quenching of turbulent magnetic diffusion is independent of magnetic Reynolds number. The situation is similar to three-dimensional MHD turbulence at large magnetic Reynolds numbers whereby the catastrophic quenching of the alpha effect does not occur when a divergence of the flux of the small-scale magnetic helicity is not zero.Comment: 8 pages, Physical Review E, in pres

Nonlinear theory of a "shear-current" effect and mean-field magnetic dynamos

The nonlinear theory of a "shear-current" effect in a nonrotating and nonhelical homogeneous turbulence with an imposed mean velocity shear is developed. The ''shear-current" effect is associated with the $\bar{\bf W} {\bf \times} \bar{\bf J}$-term in the mean electromotive force and causes the generation of the mean magnetic field even in a nonrotating and nonhelical homogeneous turbulence (where $\bar{\bf W}$ is the mean vorticity and $\bar{\bf J}$ is the mean electric current). It is found that there is no quenching of the nonlinear "shear-current" effect contrary to the quenching of the nonlinear $\alpha$-effect, the nonlinear turbulent magnetic diffusion, etc. During the nonlinear growth of the mean magnetic field, the ''shear-current" effect only changes its sign at some value $\bar{\bf B}_\ast$ of the mean magnetic field. The magnitude $\bar{\bf B}_\ast$ determines the level of the saturated mean magnetic field which is less than the equipartition field. It is shown that the background magnetic fluctuations due to the small-scale dynamo enhance the "shear-current" effect, and reduce the magnitude $\bar{\bf B}_\ast$. When the level of the background magnetic fluctuations is larger than 1/3 of the kinetic energy of the turbulence, the mean magnetic field can be generated due to the "shear-current" effect for an arbitrary exponent of the energy spectrum of the velocity fluctuations.Comment: 16 pages, 4 figures, REVTEX4, revised version, Phys. Rev. E, v. 70, in press (2004