Analysis of the effect of a mean velocity field on a mean field dynamo

We study semi-analytically and in a consistent manner the generation of a mean velocity field     by helical magnetohydrodynamical (MHD) turbulence, and the effect that this field can have on a mean field dynamo. Assuming a prescribed, maximally helical small-scale velocity field, we show that large-scale flows can be generated in MHD turbulent flows via small-scale Lorentz force. These flows back-react on the mean electromotive force of a mean field dynamo through new terms, leaving the original α and β terms explicitly unmodified. Cross-helicity plays the key role in interconnecting all the effects. In the minimal τ closure that we chose to work with, the effects are stronger for large relaxation times.