  Quasinormal modes are a set of damped resonances that describe how an excited
open system is driven back to equilibrium. In gravitational physics these modes
characterise the ringdown of a perturbed black hole, e.g. following a binary
black hole merger. A careful analysis of the ringdown spectrum reveals the
properties of the black hole, such as its angular momentum and mass. In more
complex gravitational systems the spectrum might depend on more parameters, and
hence allows us to search for new physics. In this letter we present a
hydrodynamic analogue of a rotating black hole, that illustrates how the
presence of extra structure affects the quasinormal mode spectrum. The analogy
is obtained by considering wave scattering on a draining bathtub vortex flow.
We show that due to vorticity of the background flow, the resulting field
theory corresponds to a scalar field on an effective curved spacetime which
acquires a local mass in the vortex core. The obtained quasinormal mode
spectrum exhibits long-lived trapped modes, commonly known as quasibound
states. Our findings can be tested in future experiments, building up on recent
successful implementations of analogue rotating black holes.
