Use of scattered airborne acoustic wavefield to recover profile of surface of shallow water flow

The surface of a shallow water flow is never flat. There has been strong evidence which suggests that the roughness pattern of the water surface of this type of flow is linked unambiguously to the underlying hydraulic processes. This area of research is new and there have been little or no systematic efforts to understand this link. The main interest of this paper is to investigate the interaction of airborne acoustic waves with dynamic roughness patterns and predict the key statistical and spectral characteristics of the water surface. It is proposed to use boundary integral equations approximated by Kirchhoff method1 to recover profile and statistics of randomly rough surface that is described by random process in time. In particular this numerical approach allows studying acoustic scattering from inhomogeneous roughness that supports multiple scales. Stationary phase method is suggested here to approximate the numerical solution and recover the profile of the surface. This method however is limited to the particular scale of the surface roughness but can be potentially used to retrieve non-stationary process observed on the dynamic surface in time.