A Mapping Method for Solving Dynamo Equations

Takahiro Nakajima, Paul H. Roberts

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 $\alpha ^{2}$- and $\alpha \omega $-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.