When is a sloshing vortex an analogue black hole bomb?

TL;DR

This paper investigates the conditions under which draining vortices in fluids can exhibit black hole bomb-like instabilities, especially focusing on realistic vortex cores and their analogy to gravitational phenomena.

Contribution

It introduces a variational framework to analyze vortex instabilities and identifies hollow core vortices as ideal for studying black-hole-like behaviors in fluids.

Findings

High circulation vortices exhibit black hole bomb instability mechanisms.

Low circulation vortices are unstable due to vorticity field disturbances.

Hollow core vortices are optimal for analogue gravity experiments.

Abstract

Draining vortices provide a powerful platform for simulating black hole phenomena in tabletop experiments. In realistic fluid systems confined within a finite container, low-frequency waves amplified by the vortex are reflected at the walls, rendering the system unstable. This process, known in the gravitational context as the black hole bomb, manifests as a sloshing motion of the free surface. The analogy, however, becomes more nuanced when a realistic vortex core with a non-singular vorticity distribution is considered. We investigate this by analysing a non-draining Rankine vortex in the shallow-water and inviscid limits. At low circulation, the sloshing corresponds to an instability of the vorticity field, whereas at high circulation where fluid is expelled from the vortex core, the destabilising mechanism coincides with that of the black hole bomb. Our variational framework distinguishes the energetic contributions of vorticity and irrotational perturbations, offering new insight into the rotating-polygons instability reported by, e.g. Jansson et al. (2006). From the analogue-gravity perspective, we identify hollow core vortices as an optimal regime for exploring black-hole-like instabilities in fluids.