A primer on the analogue black hole bomb with capillary-gravity waves

TL;DR

This paper studies how wave dispersion and viscosity affect the analogue black hole bomb phenomenon in draining vortices, revealing conditions for instability and implications for experiments with capillary-gravity waves.

Contribution

It provides the first detailed analysis of dispersion and viscosity effects on superradiant instabilities in analogue black hole systems with free surface vortices.

Findings

Dispersion significantly alters eigenfrequencies of unstable modes.

Viscosity mainly affects high-frequency modes.

Superradiance occurs only when circulation exceeds a certain threshold.

Abstract

Draining vortices with a free surface are frequently employed as rotating black hole simulators, both in theory and experiments. However, most theoretical work is restricted to the idealised regime, where wave dispersion and dissipation are neglected. We investigate the role of these effects on the analogue black hole bomb, an instability resulting from rotational superradiant amplification in confined systems. We reveal that the dispersion of deep water capillary-gravity waves significantly modifies the unstable mode eigenfrequencies, whereas viscosity only affects those with high frequencies. Furthermore, if the circulation is less than an order 1 multiple of the drain rate, superradiance does not occur and the vortex is stable. The instability is maximised in small systems with high flow velocities, provided there is sufficient space between the vortex and the outer boundary for the first excited state to lie inside the superradiant bandwidth. Implications for experiments on analogue black holes and free surface vortices are discussed.