Spherical Couette flow is studied with a view to elucidating the transitions between various
axisymmetric steady‐state flow configurations. A stable, equatorially asymmetric state
discovered by Bühler [Acta Mech. 81, 3 (1990)] consists of two Taylor vortices, one slightly
larger than the other and straddling the equator. By adapting a pseudospectral time‐
stepping formulation to enable stable and unstable steady states to be computed (by
Newton's method) and linear stability analysis to be conducted (by Arnoldi's method), the …