Instabilities of the Stewartson layer Part 2. Supercritical mode transitions

We investigate, both experimentally and numerically, the fluid flow in a spherical shell with radius ratio r_i/r_o=2/3. Both spheres rotate about a common axis, with _i>_o. The basic state consists of a Stewartson layer situated on the tangent cylinder, the cylinder parallel to the axis of rotation and touching the inner sphere. If the differential rotation is sufficiently large, non-axisymmetric instabilities arise, with the wavenumber of the most unstable mode increasing with increasing overall rotation. In the increasingly supercritical regime, a series of mode transitions occurs in which the wavenumber decreases again. The experimental and numerical results are in good agreement regarding this basic sequence of mode transitions, and the numerics are then used to study some of the finer details of the solutions that could not be observed in the experiment.