  We consider numerically the flow of an electrically conducting fluid in a
differentially rotating spherical shell, in a dipolar magnetic field. For
infinitesimal differential rotation the flow consists of a super-rotating
region, concentrated on the particular field line C just touching the outer
sphere, in agreement with previous results. Finite differential rotation
suppresses this super-rotation, and pushes it inward, toward the equator of the
inner sphere. For sufficiently strong differential rotation the outer boundary
layer becomes unstable, yielding time-dependent solutions. Adding an overall
rotation suppresses these instabilities again. The results are in qualitative
agreement with the DTS liquid sodium experiment.
