Construction of fast dynamos using unsteady flows and maps in three dimensions

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Abstract
Unsteady fast dynamos are constructed using a sequence of rapid movements separated by periods of diffusion of the magnetic field. Motivated by the physical mechanism described by Ze'dovich and by Soward, we examine the effect of single-mode Beltrami waves applied sequentially, and show that they can be approximated by a simple “stretch-fold-shear” (SFS) map of the unit cube onto itself. In the SFS map, the field points in a fixed direction and diffusion is easily computed. The numerical results indicate that fast dynamo action occurs for sufficiently large shear, and that the process is primarily a coherent feature of the larger magnetic scales. Similar results are obtained for smooth flows. Some preliminary analysis of the SFS map using a decomposition method is described.

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