Simulations of the anisotropic kinetic and magnetic alpha effects

TL;DR

This paper tests the minimal tau approximation in dynamo theory, showing the alpha effect's dependence on relaxation time and helicities, and examining how magnetic fields influence these processes.

Contribution

It provides a validation of the minimal tau approximation and explores the behavior of the alpha effect and helicities in anisotropic turbulence.

Findings

Relaxation time is positive and of order unity in units of turnover time.

The alpha effect is quenched by magnetic fields, largely independent of magnetic Reynolds number.

Kinetic and current helicities are dominated by large-scale flow properties.

Abstract

The validity of a closure called the minimal tau approximation (MTA), is tested in the context of dynamo theory, wherein triple correlations are assumed to provide relaxation of the turbulent electromotive force. Under MTA, the alpha effect in mean field dynamo theory becomes proportional to a relaxation time scale multiplied by the difference between kinetic and current helicities. It is shown that the value of the relaxation time is positive and, in units of the turnover time at the forcing wavenumber, it is of the order of unity. It is quenched by the magnetic field -- roughly independently of the magnetic Reynolds number. However, this independence becomes uncertain at large magnetic Reynolds number. Kinetic and current helicities are shown to be dominated by large scale properties of the flow.