  We report 3D numerical simulations of the flow of an electrically conducting
fluid in a spherical shell when a magnetic field is applied. Different
spherical Couette configurations are investigated, by varying the rotation
ratio between the inner and the outer sphere, the geometry of the imposed
field, and the magnetic boundary conditions on the inner sphere. Either a
Stewartson layer or a Shercliff layer, accompanied by a radial jet, can be
generated depending on the rotation speeds and the magnetic field strength, and
various non-axisymmetric destabilizations of the flow are observed. We show
that instabilities arising from the presence of boundaries present striking
similarities with the magnetorotational instability (MRI). To this end, we
compare our numerical results to experimental observations of the Maryland
experiment, who claimed to observe MRI in a similar setup.
