SCATTERING BY ACOUSTICALLY LARGE CORRUGATED PLANAR SURFACES

The problem of the scattering of acoustic waves by a large, sound soft (hard), corrugated surface in two dimensions is addressed. The surface undulates periodically up to a characteristic length L beyond which it becomes planar. The height of the corrugation is measured by a characteristic length a and its period by A. The ordering of these scales is taken to be A ~ A a <L, where A is the wavelength of the incident plane acoustic wave. The method of matched asymptotic expansions is applied to analyze the problem in the limit as â, = a/ L 0. This approach is both mathematically systematic and physically intuitive. The results that are obtained in the far field are identical to those obtained by using a finite beam approximation for a sound hard surface in two dimensions and almost the same for a sound soft case; the only difference being a sine factor that yields correct boundary behavior. Results for three-dimensional scattering problems are also derived and are compared similarly. © 1990, Acoustical Society of America. All rights reserved.