Nonlinear Convection in a Spherical Shell

Abstract

Nonlinear convection with spherically symmetric basic state is investigated in a thin spherical shell with rigid and nearly insulating boundaries. The nonlinear problem of steady three-dimensional convection is solved by a perturbation technique. Six physically distinct solutions are determined for the case where l=5 (l is the degree of spherical harmonics) is preferred. The preferred mode of convection is determined by a stability analysis. The axisymmetric solution is found to be unstable, while a non-axisymmetric solution which transports the maximum amount of heat appears to be preferred.