Spherical Single-Roll Dynamos at Large Magnetic Reynolds Numbers

David Ivers and Henrik Latter

Abstract

The asymptotic theory of Gilbert and Ponty (2000) for axisymmetric spherical roll flow dynamos at large magnetic Reynolds $R_m$ numbers is compared to the numerical eigen-solutions for two flows. The flows are the $s_1^0{t}_1^0$ of Dudley and James(1989) and an $s_1^0{t}_1^0{t}_3^0$ modification of it. The numerical method uses the hybrid vector spherical harmonic technique of Ivers and Phillips (2003) with fourth-order finite-differences. Excellent agreement is in the asymptotic regime $R_m>10,000$ for both the growth rate and the angular frequency. The asymptotic theory is extended to the next order.

Keywords: magnetohydrodynamics, kinematic dynamos, asymptotic theory.