We investigate analytically and numerically the dynamics of a two-dimensional superflow governed by the Gross-Pitaevskii equation passing over finite-size rectangular obstacles: an impenetrable wall and an impenetrable rectangular well. Extending classical studies of vortex nucleation around smooth obstacles, we focus on the role of sharp corners in determining the onset of vortex nucleation. Using a combination of analytical techniques based on the Schwarz-Christoffel methods for potential flow and on numerical simulations, we show that local velocity amplification near sharp corners crucially controls the critical flow velocity for vortex nucleation. For both wall and well configurations, we identify analytically and theoretically the critical velocities as a function of the obstacle width and its height or depth, finding excellent agreement between the theory and our numerical simulations. Our results provide a simple framework for understanding superflow stability past finite-size obstacles with sharp features, and they are directly relevant to experimentally realizable configurations in atomic Bose-Einstein condensates and related superfluid systems.

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• Vortices in superfluids
• Bose-Einstein condensates
• Direct numerical simulations