Minimal tau approximation and simulations of the alpha effect

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.