  We present an analysis of scattering by a fluid-mechanical `black hole
analogue', known as the draining bathtub vortex: a two-dimensional flow which
possesses both a sonic horizon and an ergoregion. We consider the scattering of
a plane wave of fixed frequency impinging upon the vortex. At low frequency, we
encounter a modified Aharonov-Bohm effect. At high frequencies, we observe
regular `orbiting' oscillations in the scattering length, due to interference
between contra-orbiting rays. We present approximate formulae for both effects,
and a selection of numerical results obtained by summing partial-wave series.
Finally, we examine interference patterns in the vicinity of the vortex, and
highlight the prospects for experimental investigation.
