  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.
