GeoFlow: On symmetry-breaking bifurcations of heated spherical shell convection

Convective motion in a spherical shell under the influence of a central force has been investigated numerically as a part of the GeoFlow experiment which will run under microgravity conditions on the International Space Station (ISS). An approach combining numerical simulations with a spectral time-stepping code and path-following techniques allows the computation of both stable and unstable solution branches of stationary states. The stability of the solutions has been determined by computing the leading eigenvalues of the Jacobian matrix. Additionally, special attention is paid to the symmetry-breaking bifurcations which are controlled by subgroups of the full spherical symmetry group O(3), under which the governing equations and the primary motionless conductive state are invariant. Finally, the transition from the stationary to the time-dependent regime is described.