Instability and Vortex Rings Dynamics in a Three-Dimensional Superfluid Flow Through a Constriction

We study the instability of a superfluid flow through a constriction in three spatial dimensions. We consider a Bose-Einstein condensate at zero temperature in two different geometries: a straight waveguide and a torus. The constriction consists of a broad, repulsive penetrable barrier. In the hydrodynamic regime, we find that the flow becomes unstable as soon as the velocity at the classical (Thomas-Fermi) surface equals the sound speed inside the constriction. At this critical point, vortex rings enter inside the bulk region of the cloud. The nucleation and dynamics scenario is strongly affected by the presence of asymmetries in the velocity and density of the background condensate flow.