Motions in a Bose condensate: VII. Boundary-layer separation

The Bose condensate model is used to analyse the superfluid flow around an ion (modelled as a solid sphere) and to elucidate the mechanism of vortex ring emission from the sphere that occurs if its velocity exceeds a critical value. An asymptotic expansion is developed for the steady subcritical flow, using the ratio of the healing length to the radius of the sphere as a small parameter. This expansion allows for the compressibility of the condensate, and converges well enough for the critical ion velocity to be calculated accurately. The flow for supercritical ion velocities is computed numerically. Particular attention is paid to the question of why the vortex rings are emitted at a preferred location on the sphere's surface.