Instabilities of magnetically induced shear layers and jets

We investigate numerically the flow of an electrically conducting fluid con fined in a spherical shell, with the inner sphere rotating, the outer spher e stationary and a strong magnetic field imposed parallel to the axis of ro tation. It has previously been shown that the axisymmetric basic state depe nds strongly on the electromagnetic boundary conditions used, with insulati ng boundaries yielding a shear layer, but conducting boundaries yielding a counter-rotating jet, where in both cases these structures are located on t he cylinder parallel to the imposed field and tangent to the inner sphere. Here we compute the non-axisymmetric instabilities of these basic states, a nd show that for sufficiently large rotation rates both the shear layer and the jet spawn a series of vortices encircling the tangent cylinder. Finall y, we consider the fully three-dimensional nonlinear equilibration, and sho w that in the supercritical regime a secondary bifurcation occurs in which the number of vortices (for the shear layer) or vortex pairs (for the jet) is reduced by one.