  Under certain conditions, sound waves in a fluid may be governed by a
Klein-Gordon equation on an `effective spacetime' determined by the background
flow properties. Here we consider the draining bathtub: a circulating, draining
flow whose effective spacetime shares key features with the rotating black hole
(Kerr) spacetime. We present a complete investigation of the role of
quasinormal (QN) mode and Regge pole (RP) resonances of this system. First, we
simulate a perturbation in the time domain by applying a finite-difference
method, to demonstrate the ubiquity of `QN ringing'. Next, we solve the wave
equation in the frequency domain with the continued-fraction method, to compute
QN and RP spectra numerically. We then explore the geometric link between
(prograde and retrograde) null geodesic orbits on the spacetime, and the
properties of the QN/RP spectra. We develop a `geodesic expansion' method which
leads to asymptotic expressions (in inverse powers of mode number $m$) for the
spectra, the radial functions and the residues. Next, the role of the Regge
poles in scattering and absorption processes is revealed through application of
the complex angular momentum method. We elucidate the link between the Regge
poles and oscillations in the absorption cross section. Finally, we show that
Regge poles provide a neat explanation for `orbiting' oscillations seen in the
scattering cross section.

General Relativity and Quantum Cosmology