Superflows around corners

TL;DR

This paper combines analytical and numerical methods to study how sharp corners on finite obstacles influence vortex nucleation in superflows governed by the Gross-Pitaevskii equation, with implications for superfluid stability.

Contribution

It introduces a framework linking corner geometry to critical velocities for vortex nucleation, extending classical smooth obstacle studies to sharp-edged structures.

Findings

Critical velocities depend on obstacle width and height/depth.

Sharp corners significantly amplify local flow velocity.

Theory matches well with numerical simulations.

Abstract

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 an 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 are directly relevant to experimentally realizable configurations in atomic Bose-Einstein condensates and related superfluid systems.