Instabilities of magnetically induced shear layers and jets

We investigate numerically the flow of an electrically conducting fluid confined in a spherical shell, with the inner sphere rotating, the outer sphere stationary, and a strong magnetic field imposed parallel to the axis of rotation. It has previously been shown that the axisymmetric basic state depends strongly on the electromagnetic boundary conditions used, with insulating boundaries yielding a shear layer, but conducting boundaries yielding a counter–rotating jet, where in both cases these structures are located on the cylinder parallel to the imposed field and tangent to the inner sphere. Here we compute the non–axisymmetric instabilities of these basic states, and show that for sufficiently large rotation rates both the shear layer and the jet spawn a series of vortices encircling the tangent cylinder. Finally, we consider the fully three–dimensional nonlinear equilibration, and show 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.