  We present axisymmetric numerical calculations of the fluid flow induced in a
spherical shell with inner sphere rotating and outer sphere stationary. A
magnetic field is also imposed, consisting of particular linear combinations of
axial and dipolar fields, chosen to make $B_r=0$ at either the outer sphere, or
the inner, or in between. This leads to the formation of Shercliff shear layers
at these particular locations. We then consider the effect of increasingly
large inertial effects, and show that an outer Shercliff layer is eventually
de-stabilized, an inner Shercliff layer appears to remain stable, and an
in-between Shercliff layer is almost completely disrupted even before the onset
of time-dependence, which does eventually occur though.

Earth and Planetary Astrophysics;Fluid Dynamics;Geophysics