Theory of acoustic radiation near a hyperbolic ridge

Abstract

A solution to the acoustic field due to a harmonic point source near a hyperbolic ridge with perfectly reflecting boundaries in an isovelocity ocean is derived and developed. An exact expression for the field is given as a modal sum of integrals. The integrals are in terms of eigenfunctions of the reduced wave equation in the three-dimensional elliptical coordinate system. The eigenfunctions are approximated away from the low-frequency limit by standard WKB techniques. The resulting integrals are estimated by first and second order stationary phase asymptotics, which are matched in the vicinity of the caustics, yielding a complete representation of the field. The field is given in terms of standard elliptic functions for which fast numerical routines are available. The solution includes the locations of the caustics and shadow zones, as well as predicting a complicated intramodal interference pattern resulting from the intersection of up to three rays in a given mode. The explicit representation of these features arising from horizontal refraction makes this theoretical model useful as a new fully three-dimensional benchmark solution.