Dynamo Action in the Presence of an Imposed Magnetic Field

Details Dynamo Action in the Presence of an Imposed Magnetic Field Dynamo Action in the Presence of an Imposed Magnetic Field

2009-01-23

arxiv.org/abs/0901.3734v1

Proc. Roy. Soc. A 465, 1599 (2009)

Physics

Fluid Dynamics

18 pages, 8 figures, submitted to Proc Roy Soc A

Scientific paper

10.1098/rspa.2008.0493

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 $Rm \to \infty$.

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