Alpha tensor and dynamo excitation in turbulent fluids with anisotropic conductivity fluctuations

Abstract

A mean-field theory of the electrodynamics of a turbulent fluid is formulated under the assumption that the molecular electric conductivity is correlated with the turbulent velocity fluctuation in the (radial) direction, (Formula presented.). It is shown that for such homogeneous fluids a strong turbulence-induced field advection anti-parallel to (Formula presented.) arises almost independently of rotation. For rotating fluids, an extra (Formula presented.) effect appears with the known symmetries and with the expected maximum at the poles. Fast rotation, however, with Coriolis number exceeding unity suppresses this term. Numerical simulations of forced turbulence using the nirvana code demonstrate that the radial advection velocity, (Formula presented.), always dominates the (Formula presented.) term. We show finally with simplified models that (Formula presented.) dynamos are strongly influenced by the radial pumping: for (Formula presented.) the solutions become oscillatory, while for (Formula presented.) they become highly exotic if they exist at all. In conclusion, dynamo models for slow and fast solid-body rotation on the basis of finite conductivity–velocity correlations are unlikely to work, at least for (Formula presented.) dynamos without strong shear.