Phase mixed rotating magnetoconvection and Taylor's condition I. Amplitude equations

Abstract

Abstract Fluid of density ρ, kinematic viscosity v, electrical conductivity [sgrave] rotates rapidly with angular velocity ω and is permeated by an axisymmetric azimuthal magnetic field B. Boussinesq convection is considered in a self-gravitating sphere, radius R, which results from an unstable radial density gradient. At small values of the Elsasser number Λ(= [sgrave]B 2/2ρω), convection is localised close to a cylinder with generators parallel to the rotation axis. The qualitative features of such convection are adequately reproduced by Busse's annulus model. Here attention is restricted to the magnetostrophic regime. E⅓ ≪ Λ ≪ 1 [Ekman number, E(= v/ωR)], for which the rotational constraints are partially relaxed by the Lorentz forces. Marginal convection is characterised by axial roll-like travelling waves of short azimuthal length scale. An equation governing the radial modulation of the convective amplitude is derived, which involves advection by the geostrophic flow and the influence of phase mixin...