Dynamo Action in the Presence of an Imposed Magnetic Field

TL;DR

This paper investigates how an imposed magnetic field influences the linear stability of magnetohydrodynamic flows, revealing that such a field generally stabilizes the flow and affects the growth rate of perturbations.

Contribution

It provides a detailed analysis of the stability of MHD flows with an imposed magnetic field, highlighting the stabilizing effect and the behavior of growth rates at high magnetic Reynolds numbers.

Findings

Imposed magnetic fields stabilize the flow at a given magnetic Reynolds number.

Growth rates of unstable perturbations become independent of Rm at high Rm.

Background magnetic fields influence the properties and stability of MHD basic states.

Abstract

We consider the linear stability to three-dimensional perturbations of two-dimensional nonlinear magnetohydrodynamic basic states obtained from a specified forcing function in the presence of an imposed initially uniform magnetic field of strength $B_0$. The forcing is chosen such that it drives the CP flow of Galloway & Proctor (1992) when $B_0=0$. We first examine the properties of these basic states and their dependence on $B_0$ and on the magnetic Reynolds number $Rm$. The linear stability of these states is then investigated. It is found that at a given $Rm$ the presence of a background field is stabilising. The results also allow us to speculate that at a fixed value of $B_0$ the growth of the unstable perturbations is `fast', in the sense that the growth rate becomes independent of $Rm$ as $Rm \to \infty$.