Effect of Differential Rotation on Nonlinear Mean Electromotive Force in a Turbulent Flow

An effect of a mean differential rotation on the nonlinear mean electromotive force in a turbulent flow is studied. An interaction of the mean differential rotation (i.e., a mean velocity shear) with a small-scale turbulent motions can cause a generation of a mean magnetic field even in a nonhelical turbulent fluid flow. This mechanism of a mean-field dynamo is associated with a ”shear-current” effect which is determined by the W̄×J̄ term in the mean electromotive force (where W̄ is the mean vorticity caused by the mean differential rotation and J̄ is the mean electric current). We demonstrated that the nonlinear ”shear-current” effect comprises one of the main nonlinearities in a mean-field dynamo, e.g., it determines the level of the saturated mean magnetic field. During the nonlinear growth of the mean magnetic field, the ”shear-current” effect changes its sign, but there is no quenching of this effect contrary to the quenching of the nonlinear α effect, the nonlinear turbulent magnetic diffusion, the nonlinear Ω×J̄ effect, etc. We found that in the spherical and cylindrical geometries the ”shear-current” effect causes also a nonhelical α effect which is independent of a hydrodynamic helicity. The nonhelical α effect vanishes when the rotation is constant on the cylinders which are parallel to the rotation axis. The above new effects determine the nonlinear evolution of the mean magnetic field. We studied the nonlinear ”shear-current” effect, the nonhelical α effect and the nonlinear Ω×J̄ effect using the τ -approximation (the Orszag third-order closure procedure). Astrophysical applications of these effects are discussed.