Coherence function for the stochastic scattering by atime-varying, slightly rough, acoustically soft surface

摘要

Approximations for the coherence function of the random acoustic field scattered by a moving roughsurface are extracted from a second-order perturbation expansion. The statistically rough surface ischaracterized by a simple, wide-sense stationary autocorrelation function that exhibits temporal andspatial dispersive behavior in terms of three parameters: the acoustically-small mean-square surfaceheight, a correlation length, and a group velocity. Excitation is provided by the quintessentialobliquely-incident time-harmonic plane-wave. Asymptotic evaluation of Fourier integralrepresentations of the stochastic field yields expressions for the coherence function that explicitlydisplay the dependence upon the space and time coordinates and their interaction via the geometricalparameters of the rough surface.