Superflow passing over a rough surface: Vortex nucleation

The transition from a free vortex superflow to a dissipative vortex flow in a superfluid remains an open problem, in particular because in real experiments, microscopic asperities on the walls play a major role since the relevant scales in a superfluid motion are basically of atomic scale. Here we model a superflow using the Gross-Pitaevskii mean-field equation in a domain with a rigid sinusoidal boundary. We demonstrate, analytically and numerically, the existence of a well-defined critical velocity for vortex nucleation. Additionally, we discuss the intrinsic mechanism of vortex nucleation by the appearance of a solitary wave characterized by a depletion of the wave function near the boundary.