Scattering by a draining bathtub vortex

TL;DR

This paper analyzes wave scattering by a draining bathtub vortex, revealing phenomena like a modified Aharonov-Bohm effect and orbiting oscillations, with implications for experimental fluid dynamics analogues of black holes.

Contribution

It provides the first detailed analysis of wave scattering phenomena in a draining bathtub vortex, including approximate formulas and numerical results for interference effects.

Findings

Modified Aharonov-Bohm effect at low frequencies

Orbiting oscillations at high frequencies

Potential for experimental observation of scattering patterns

Abstract

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.