Acoustic scattering from a rough sphere

Abstract

The scattering of a plane acoustic wave from a random rough sphere is studied using the null field approach. The starting point is an integral representation derived from the Helmholtz equation. The incident field, the scattered field, and the free-space Green’s function are all expanded in terms of suitably chosen basis functions. In this way a relation between the incident and the scattered fields is obtained, which is expressed by the transition matrix (T matrix). The scattered field is expanded in a power series of a small parameter, namely the product of the wave number and the root-mean-square height of the irregularities. Analytical expressions for the leading terms of the series have been calculated. In particular, ensemble averages of the far-field amplitude and the scattering cross section have been determined. As the analytical results are somewhat complicated, some numerical results are presented. Numerical computations of higher-order terms indicate that the convergence of the series is satisfactory as long as the root-mean-square height is small compared to a correlation length describing the average distance between the peaks of the surface.