Interplay of Kelvin-Helmholtz and superradiant instabilities of an array of quantized vortices in a two-dimensional Bose--Einstein condensate

TL;DR

This paper explores the complex instabilities in a vortex array within a 2D Bose-Einstein condensate, revealing different dominant mechanisms across flow regimes, including Kelvin-Helmholtz, superradiant, and boundary-related instabilities.

Contribution

It identifies and characterizes multiple instability mechanisms in vortex arrays, highlighting their dependence on flow velocity and system size, and introduces the interplay between hydrodynamic and radiative effects.

Findings

Kelvin-Helmholtz instability dominates at subsonic velocities.

Superradiant scattering suppresses KHI at supersonic velocities.

Boundary-induced displacement instability occurs at slow velocities.

Abstract

We investigate the various physical mechanisms that underlie the dynamical instability of a quantized vortex array at the interface between two counter-propagating superflows in a two-dimensional Bose--Einstein condensate. Instabilities of markedly different nature are found to dominate in different flow velocity regimes. For moderate velocities where the two flows are subsonic, the vortex lattice displays a quantized version of the hydrodynamic Kelvin--Helmholtz instability (KHI), with the vortices rolling up and co-rotating. For supersonic flow velocities, the oscillation involved in the KHI can resonantly couple to acoustic excitations propagating away in the bulk fluid on both sides. This makes the KHI rate to be effectively suppressed and other mechanisms to dominate: For finite and relatively small systems along the transverse direction, the instability involves a repeated superradiant scattering of sound waves off the vortex lattice; for transversally unbound systems, a radiative instability dominates, leading to the simultaneous growth of a localized wave along the vortex lattice and of acoustic excitations propagating away in the bulk. Finally, for slow velocities, where the KHI rate is intrinsically slow, another instability associated to the rigid lateral displacement of the vortex lattice due to the vicinity of the system's boundary is found to dominate.