Spherical single-roll dynamos at large magnetic Reynolds numbers

TL;DR

This study investigates spherical helical dynamos at high magnetic Reynolds numbers, demonstrating numerical solutions align with asymptotic theory predictions for growth rates and eigenfunctions at large m.

Contribution

It provides numerical validation of asymptotic theory for spherical dynamos at large magnetic Reynolds numbers, focusing on single-roll flows.

Findings

Good agreement of growth rates for m>10^4

Eigenfunctions match asymptotic predictions for m>10^5

Numerical solutions confirm theoretical models at high m

Abstract

This paper concerns kinematic helical dynamos in a spherical fluid body surrounded by an insulator. In particular, we examine their behaviour in the regime of large magnetic Reynolds number $\Rm$, for which dynamo action is usually concentrated upon a simple resonant stream-surface. The dynamo eigensolutions are computed numerically for two representative single-roll flows using a compact spherical harmonic decomposition and fourth-order finite-differences in radius. These solutions are then compared with the growth rates and eigenfunctions of the Gilbert and Ponty (2000) large $\Rm$ asymptotic theory. We find good agreement between the growth rates when $\Rm>10^4$, and between the eigenfunctions when $\Rm>10^5$.