The mean electro-motive force, current- and cross-helicity under the influence of rotation, magnetic field and shear

The mean electromotive force (MEMF) in a rotating stratified magnetohydrodynamical turbulence is studied.Our study rests on the mean-field magnetohydrodynamics framework and $\tau$ approximation. We compute the effects of the large-scale magnetic fields (LSMF), global rotation and large-scale shear flow on the different parts of the MEMF (such as $\alpha$ - effect, turbulent diffusion, turbulent transport, etc.) in an explicit form. The influence of the helical magnetic fluctuations which stem from the small-scale dynamo is taken into account, as well. In the paper, we derive the equation governing the current helicity evolution. It is shown that the joint effect of the differential rotation and magnetic fluctuations in the stratified media can be responsible for the generation, maintenance and redistribution of the current helicity. The implication of the obtained results to astrophysical dynamos is considered as well.