Asymptotic theory of scattering by a rough surface progressing over an inhomogeneous ocean

Abstract

An asymptotic theory of scattering by a rough surface is presented which is appropriate to small ocean surface wave heights and valid for a slowly varying refractive index. The ocean surface is described as a sum of gravity waves of varying frequency progressing in different directions. It is demonstrated that, to a given order of approximation in the asymptotic theory, the average energy associated with the sideband rays is precisely accounted for by a reduction in intensity of the reflected carrier. The theory is shown to be in complete agreement with results obtained by asymptotic analysis of exact integral representations for the case of an isovelocity ocean. Wavenumber diagrams are introduced which are extremely useful for depicting the directions of the incident and scattered rays at the surface, demonstrating the effect of varying surface wave and acoustic frequency and demonstrating the frequency cutoff of the sideband power spectrum. It is shown how the theory can accommodate the effects of energy focusing, both in the carrier and sidebands, through the use of known uniformly valid asymptotic expansions of the field in the presence of caustics. [Research supported by the Office of Naval Research, Code 480.]