On Adiabatic Sound Propagation in a Shallow Sea with a Circular Underwater Canyon

Abstract

An idealized problem of sound propagation in a shallow sea with a curved underwater canyon is considered. The canyon is a circular feature of the bottom relief which causes horizontal refraction of acoustic waves. The sound field computation method for a waveguide with an inhomogeneity of this type is considered, and the geometry of horizontal rays trapped by the canyon is studied. The computation method is based on the separation of variables in the equation for the mode amplitudes and representation of the solution in the form of a double series. This technique is rather general in nature, because it can be used to compute the field in any problem where the waveguide has rotational symmetry. Furthermore, it is also shown which terms of the series correspond to horizontal rays trapped by the canyon.