The first instability in spherical Taylor-Couette flow

In this paper continuation methods are applied to the axisymmetric Navier-Stokes equations in order to investigate how the stability of spherical Couette flow depends on the gap size σ. We find that the flow loses its stability due to symmetry-breaking bifurcations and exhibits a transition with hysteresis into a flow with one pair of Taylor vortices if the gap size is sufficiently small, i.e. if σ ≤σ_B. In wider gaps, i.e. for σ_B σ_F. The numbers σ_B and σ_F are computed by calculating the instability region of the spherical Couette flow and the region of existence of the flow with one pair of Taylor vortices