PHASE MIXED ROTATING MAGNETOCONVECTION AND TAYLORS CONDITION .1. AMPLITUDE EQUATIONS

Fluid of density rho, kinematic viscosity nu, electrical conductivity sigma rotates rapidly with angular velocity Omega and is permeated by an axisymmetric azimuthal magnetic field B. Boussinesq convection is c onsidered in a self-gravitating sphere, radius R, which results from a n unstable radial density gradient. At small values of the Elsasser nu mber Lambda(= sigma B-2/2 rho Omega), convection is localised close to a cylinder with generators parallel to the rotation axis. The qualita tive features of such convection are adequately reproduced by Busse's annulus model. Here attention is restricted to the magnetostrophic reg ime. E(1/3) much less than Lambda much less than 1 [Ekman number, E(= nu/Omega R(2))], for which the rotational constraints are partially re laxed by the Lorentz forces. Marginal convection is characterised by a xial roll-like travelling waves of short azimuthal length scale. An eq uation governing the radial modulation of the convective amplitude is derived, which involves advection by the geostrophic flow and the infl uence of phase mixing. The former geostrophic how is driven nonlinearl y by the Lorentz force resulting from the magnetic field pertubations caused by the convection but damped linearly by Ekman suction at the b oundary; the viscously modified Taylor's condition. The latter phase m ixing results because the local convection frequency varies radially. A few preliminary results are obtained.