Scattering of surface shallow water waves on a draining bathtub vortex

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.