Sound scattering from a randomly rough fluid–solid interface

A general formalism for acoustic scattering from a fluid–elastic solid interface is developed. The theory parallels Waterman’s work [P. C. Waterman, J. Acoust. Soc. Am. 45, 1417 (1969)], based on the extinction theorem, for acoustic scattering from impenetrable surfaces. This formalism is then used to study the scattering of sound waves from a randomly rough fluid–solid interface by using perturbation theory to solve the equations for the scattering amplitudes to second order. The Watson–Keller renormalization ansatz [J. G. Watson and J. B. Keller, J. Acoust. Soc. Am. 74, 1887 (1983)] is then used to account for some multiple scattering effects beyond double scattering. A numerical study is presented comparing acoustic scattering in the fluid from a fluid–solid interface with acoustic scattering in the same fluid from a hard, impenetrable surface (Neumann boundary condition). Substantial differences between the two cases are found. Besides the expected acoustic energy loss by transmission into the solid, it was also found that the angular distribution of the remaining acoustic energy that is reflected and scattered by the fluid–solid interface differs greatly from the hard impenetrable surface case, especially near grazing incidence and scattering angles.