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 (W) over bar X (J) over bar term in the mean electromotive force and causes the generation of the mean magnetic field even in a nonrotating and nonhelical homogeneous turbulence (where (W) over bar is the mean vorticity and (J) over bar 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 (B) over bar (*) of the mean magnetic field. The magnitude (B) over bar (*) 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 (B) over bar (*). 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.