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 $\overline{\mathbf{W}}\times \overline{\mathbf{J}}$ term in the mean electromotive force and causes the generation of the mean magnetic field even in a nonrotating and nonhelical homogeneous turbulence (where $\overline{\mathbf{W}}$ is the mean vorticity and $\overline{\mathbf{J}}$ 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 ${\overline{\mathbf{B}}}_{*}$ of the mean magnetic field. The magnitude ${\overline{\mathbf{B}}}_{*}$ 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 ${\overline{\mathbf{B}}}_{*}$. 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.

• Received 15 June 2004

DOI:https://doi.org/10.1103/PhysRevE.70.046310