Acoustic scattering by two-dimensionally rough interfaces between dissipative acoustic media—Full wave, physical acoustics, and perturbation solutions

Abstract

Explicit expressions for the acoustic pressure and velocity scattered by two-dimensionally rough surfaces are derived using a full-wave approach. The conditions under which these solutions merge with the physical acoustic and small perturbation solutions in the high- and low-frequency limits are given. The acoustic media on both sides of the rough interface are characterized by their bulk modulus, equilibrium density, and relaxation time (to account for dissipation); the Dirichlet and Neumann boundary conditions are treated as special cases. The closed-form full-wave expressions for the surface element scattering coefficients are significantly different for these special cases. However, the corresponding physical optics solutions differ only in the sign of the acoustic reflection coefficient. The full-wave solution can be applied to composite surfaces with a broad range of roughness scales. Since it accounts for specular point and diffuse scattering in a unified self-consistent manner, there is no need to adopt a two-scale model of the rough surface. Thus the full-wave expressions for the rough surface scattered fields are also more suitable for application to broadband (transient) excitation problems and for the solution of inverse problems.