Non-axisymmetric instabilities in magnetic spherical Couette flow

We investigate numerically the flow of an electrically conducting fluid confined in a spherical shell, with the outer sphere stationary, the inner sphere rotating and a magnetic field imposed parallel to the rotation axis. We compute both the axisymmetric basic states and their non-axisymmetric instabilities. Two distinct instability classes emerge, one connected to previous non-magnetic results, the other to previous strongly magnetic results. Both instabilities arise from the basic state's meridional circulation, but are otherwise very different from one another, and are separated by a region of stability that persists even for large Reynolds numbers. Finally, we compute the fully three-dimensional nonlinear equilibration of both instabilities. The second class exhibits a rich variety of secondary bifurcations, involving mode transitions between different azimuthal wave numbers.