Numerical simulation of the Gailitis dynamo

Abstract

The linear magnetohydrodynamic equations are solved with vacuum surface boundary conditions in a thick spherical shell, where the only fluid motions are meridional “rolls”. These motions are similar to those studied by Gailitis (Gailitis, A., Self-excitation of a magnetic field by a pair of annular vortices. Mag. Gidrod., 1970, 6, 19–22 (English translation: Magnetohydrodynamics, 1970, 6, 14–17).), except that in that paper the motions were confined to toroidal annuli, with minor and major axes a and c respectively, and a/c≪1. The seminal result of Gailitis, that such motions excite magnetic fields with axis of symmetry perpendicular to the axis of symmetry of the velocity field, is illustrated for cases where Gailitis's conditions are relaxed. In particular, the parity properties of the dynamo-generated fields depend on the sense of the fluid motions in the same manner as found by Gailitis. An attempt is made to compare predicted and computed marginal dynamo numbers, and a plausible agreement is obtained. Finally, when the parity of the fluid motion is reversed, a new class of nonaxisymmetric oscillatory dynamo solutions is obtained.

Keywords:

• Magnetic fields
• MHD
• Gailitis dynamo
• Dynamo theory

Acknowledgements

Thanks are due to Leon Mestel and Dmitri Sokoloff for comments on a draft version of this article. The final version was also improved by the reports from anonymous referees.