Validity of the sonar equation and Babinet’s principle for object scattering in a shallow water waveguide

Abstract

It has recently been shown that the sonar equation can provide a reasonable approximation to nonforward scattering from a noncompact (ka>1) sphere submerged in an ocean waveguide. The omnidirectional scattering characteristics of the sphere in nonforward directions enables the sphere’s far-field plane wave scattering function to be factored in the single-scatter waveguide solution just as it is in free space. The highly directional nature of the sphere’s scattering in the forward direction, however, prevents this factorization and leads to significant departures from sonar equation predictions in the forward direction. By Babinet’s principle, the forward scattered field from a noncompact sphere subject to an incident plane wave in free space will be nearly the same as that of a disk of the same projected area. Accordingly, it is shown that the sonar equation can significantly overestimate the field scattered from an upright plate or disk submerged in an ocean waveguide. These flat objects yield some of the most directional scattering possible from a finite body. It is also shown that in an ocean waveguide the upright disk and an equivalently located sphere with the same great circle area can have nearly identical forward scattered fields, just as in free space.