Critical velocity for wake vortex generation behind a plate in a superflow

TL;DR

This paper theoretically investigates the critical velocity for quantum vortex generation behind a moving plate in a Bose-Einstein condensate, revealing size-dependent behavior and the importance of compressibility effects.

Contribution

It introduces a perturbative approach incorporating compressibility into potential flow theory to accurately predict critical velocities.

Findings

Critical velocity decreases with increasing plate size.

Asymptotic behavior of critical velocity follows $L^{-1/2}$ for large plates.

Finite plate thickness increases the critical velocity.

Abstract

We study theoretically the critical velocity $U_c$ for quantum vortex generation by a thin plate-shaped obstacle moving through a uniform Bose-Einstein condensate. Our results based on the Gross-Pitaevskii theory reveal that the critical velocity monotonically decreases with increasing plate size $L$. In the limit of large $L$, the critical velocity is asymptotic to $L^{-1/2}$ predicted by the potential flow theory for an incompressible ideal fluid with a phenomenological length correction. As $L$ decreases, however, the incompressible analysis breaks down quantitatively. By performing a perturbative analysis to incorporate compressibility into the potential flow theory, we have successfully reproduced the numerical results analytically over a wide parameter range. It is also shown that the critical velocity increases with finite plate thickness.