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

TL;DR

This paper develops a mean-field theory for turbulent fluids with anisotropic conductivity, revealing turbulence-induced magnetic field advection and the influence of radial pumping on dynamo behavior, supported by numerical simulations.

Contribution

It introduces a new mean-field model considering conductivity-velocity correlations and demonstrates their impact on dynamo mechanisms in turbulent fluids.

Findings

Radial advection dominates over the $oldsymbol{ ext{alpha}}$ effect.

Fast rotation suppresses the $oldsymbol{ ext{alpha}}$ effect.

Radial pumping significantly influences $oldsymbol{ ext{alpha}}^2$ dynamo solutions.

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, $\mathbf{g}$. It is shown that for such homogeneous fluids a strong turbulence-induced field advection anti-parallel to $\mathbf{g}$ arises almost independently of rotation. For rotating fluids, an extra $\alpha$ 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, $\gamma$, always dominates the $\alpha$ term. We show finally with simplified models that $\alpha^2$ dynamos are strongly influenced by the radial pumping: for $\gamma<\alpha$ the solutions become oscillatory, while for $\gamma>\alpha$ 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 $\alpha^2\Omega$ dynamos without strong shear.