## 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 $$s^0_1t^0_1$$ of Dudley and James(1989) and an $$s^0_1t^0_1t^0_3$$ 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.

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 Tuesday, May 20, 2008