Bifurcations in rotating spherical shell convection under the influence of differential rotation.

Abstract

The bifurcations of thermal convection in a rotating spherical shell heated from the inner sphere and driven by the buoyancy of a central gravity field are studied numerically. This model of spherical Rayleigh-Bénard convection describes large-scale convection in planets and in the outer zones of celestial bodies. In this work, the influence of an additionally imposed differential rotation of the inner sphere with respect to the outer one on the heat transfer and, more generally, on the whole bifurcation structure is investigated. In addition to numerical simulations, path-following techniques are applied in order to compute both stable and unstable solution branches. The dynamics and the heat transfer are essentially determined by a global bifurcation, which we have identified as a homoclinic bifurcation that consists of a collision of a stable modulated rotating with an unstable rotating wave.