Numerical studies of rough surface scattering models

Abstract

In recent years a number of rough surface scattering models have been introduced that attempt to “bridge the gap” between the classical perturbation and Kirchhoff approximations. Among these are the phase perturbation technique and the small slope approximation. Investigations have shown that for pressure-release surfaces with a Gaussian roughness spectrum, the phase perturbation model is accurate in cases when the classical approximations fail. Monte Carlo calculations by Betman for the second-order small slope approximation show excellent agreement with results obtained using the Rayleigh-Fourier method both for wind-driven sea surfaces and for the fluid-solid boundary condition. In this work, the first- and second-order small slope approximation reflection coefficients and bistatic scattering cross sections are derived for the Dirichlet (pressure-release) problem. The first-order results are shown to reduce to those of the perturbation and Kirchhoff methods for the reflection coefficient and to that of the perturbation method for the bistatic scattering cross section. In addition, phase perturbation results are calculated for a multiscale (Pierson-Moskowitz) surface spectrum. For both models, numerical results for one-dimensional, pressure-release surfaces with a Pierson-Moskowitz spectrum are compared with exact numerical results obtained using a Monte Carlo technique.