Primer on the analog black hole bomb with capillary-gravity waves

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 idealized regime, where wave dispersion and dissipation are neglected. We investigate the role of these effects on the analog 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 maximized 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 analog black holes and free surface vortices are discussed. Published by the American Physical Society 2024