The Strong Field Branch of the Childress–Soward Dynamo

Summary

The Childress–Soward dynamo, which uses rotating Benard convection to maintain a magnetic field against Ohmic decay, is investigated numerically. A converged three-dimensional solution of the strong field branch is presented for very small Ekman number. For strong rotation, the system is able sustain convection and act as a dynamo even for a Rayleigh number substantially less than critical. It is found that the dominant forces tend to cancel, and that the magnitudes of the curls of the Lorentz and Coriolis forces remain virtually identical.

INTRODUCTION

Numerical computations comprise an increasingly important tool in the understanding of the Earth's dynamo, and, with the increased accessibility of supercomputers, direct, realistic simulations of the geodynamo are not far off. Any such simulation must solve the equations governing a three dimensional, rapidly rotating, dynamically consistent dynamo with Lorentz force J × B present in the dominant balance of forces. The simplest dynamo with these characteristics, first proposed by Childress & Soward (1972), uses the convective motions of rapidly rotating Benard convection to drive a dynamically consistent MHD dynamo. Computationally, the Childress–Soward dynamo has the advantage of permitting the expansion of the unknown fields in Fourier series in all directions, allowing three dimensional fast Fourier transforms (FFT's) to be used in calculating the nonlinear terms. Since no fast Legendre transform exists at the moment, the resulting programs will be faster than more realistic spherical dynamo simulations, while at the same time reflecting the important features of these models.

In this paper, the strong field branch of the Childress–Soward dynamo is investigated using direct numerical simulations.