Scattering of surface shallow water waves on a draining bathtub vortex

TL;DR

This paper models how shallow water surface waves scatter on a draining vortex, drawing parallels to wave behavior near rotating black holes, and provides analytical and numerical solutions for different frequency regimes.

Contribution

It introduces a linear model for wave scattering on a draining vortex, including analytic solutions for low frequencies and numerical analysis for moderate frequencies, highlighting vortex-wave interactions.

Findings

Analytic solutions for low-frequency wave scattering.

Numerical solutions for moderate frequencies.

Identification of vortex-induced wave emission processes.

Abstract

In the linear approximation we study long wave scattering on an axially symmetric flow in a shallow water basin with a drain in the center. This classical problem can be considered as a model of wave scattering on a rotating black hole. For the low frequencies analytic solutions are derived to describe both pure potential perturbations (surface gravity waves), and perturbations with nonzero potential vorticity. For moderate frequencies such solutions are obtained numerically and illustrated graphically. It is shown that there are two processes governing the dynamics of perturbations, namely, the scattering of incident gravity waves by central vortex, and the emission of gravity waves stimulated by the potential vorticity. Some aspects of their joint action are discussed.