Whispering gallery waves localized near circular isobaths in shallow water

Sound propagation in an area of shallow sea with circular isobaths and the bottom depth increasing towards their curvature center is considered. Such an area could be part of a bay, a lagoon, or a lake with bowl-like bottom relief. The possible formation of whispering gallery waves localized in the vicinity of curved isobaths is considered. Simple criteria for the formation of such whispering gallery due to horizontal refraction are derived; their transverse modal structure is described analytically in terms of Bessel functions and using the Wentzel-Kramers-Brillouin-Jeffreys approximation. The corresponding azimuthal wavenumbers and radial mode functions are computed. Dispersion of such waves is also investigated, and the possibility of their experimental observation is discussed.