A mapping method for solving dynamo equations

Abstract

A new method is presented for integration of the equations of magnetohydrody­namics in rapidly rotating, electrically conducting fluids, and in particular for studying dynamo action in such systems. Tests of the method are reported. The decay rate of magnetic field in a stationary sphere are recovered, as are the results of a number of α 2 - and αω -dynamos. These are solutions of the electrodynamic (induction) equation. An intermediate dynamo model, in which the dynamics are also partly allowed for, is also studied. This is due to Braginsky ( Geomag. Aero­naut . 18, 225 (1978)) and is of ‘model- Z type’. All models considered here are axisymmetric, but the possibility of generalization to three-dimensions is allowed for.