Convection in a rapidly rotating spherical shell at infinite Prandtl number: steadily drifting rolls

Abstract

Three-dimensional linear and non-linear convection at infinite Prandtl number in a rapidly rotating spherical fluid shell of radius ratio η = r i r o = 0.4 is investigated numerically. An asymptotic criterion for the onset of convective instability (at large Taylor number) is derived, and the asymptotic relationship describing the typical finite amplitude of steadily drifting rolls, U, the Rayleigh number, R, and the Taylor number, T, U = 20.1(R/T 2 3 − 1.63) 1 2 = 25.6[ ( R − R c ) R c ) ] 1 2 is obtained from non-linear solutions of the full equations. A particularly interesting feature of the finite amplitude convection is the formation of the double-layer structure of the temperature field (with respect to the basic state); the spherically symmetric basic distribution of the buoyancy force is therefore strongly modified. As a consequence, the linear convection columnar rolls positioned at mid-latitudes are moved to much lower latitudes at finite amplitudes. Instead of transporting heat into the narrow belt of the top and bottom of the convection cylinder at small amplitudes, the non-linear convection transfers heat much more effectively in the large equatorial area, reflecting the way in which the non-linear effects overcome the constraints of rotation.