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.