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

The nonlinear theory of a "shear-current" effect in a 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). We found that there are 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. We showed that the magnitude $\bar{\bf B}_\ast$ determines the level of the saturated mean magnetic field which is less than the equipartition field. We found that the background magnetic fluctuations due to the small-scale dynamo enhance the "shear-current" effect, and cause decrease the magnitude $\bar{\bf B}_\ast$. We demonstrated that 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. Astrophysical applications of the obtained results are discussed.