Magnetic instabilities in rapidly rotating spherical geometries. III. The effect of differential rotation

Abstract

Abstract We investigate the influence of differential rotation on magnetic instabilities for an electrically conducting fluid in the presence of a toroidal basic state of magnetic field B 0 = BMB0(r, θ)1 φ and flow U0 = UMU0 (r, θ)1φ, [(r, θ, φ) are spherical polar coordinates]. The fluid is confined in a rapidly rotating, electrically insulating, rigid spherical container. In the first instance the influence of differential rotation on established magnetic instabilities is studied. These can belong to either the ideal or the resistive class, both of which have been the subject of extensive research in parts I and II of this series. It was found there, that in the absence of differential rotation, ideal modes (driven by gradients of B 0) become unstable for Ac ≳ 200 whereas resistive instabilities (generated by magnetic reconnection processes near critical levels, i.e. zeros of B0) require Ac ≳ 50. Here, Λ is the Elsasser number, a measure of the magnetic field strength and Λc is its critical value at mar...