Coherent sound scatter from a rough interface between arbitrary fluids with particular reference to roughness element shapes and corrugated surfaces
Authors: Tolstoy I. 
Published: October 2005

The theory of Biot scatter, previously formulated for small hemispherical or almost hemispherical roughness elements on a hard wall or on an interface between fluids of differing densities ρ1≠ρ2 but same sound velocity c1 = c2, is here extended to more general cases ρ1≠ρ2, c1 = c2 involving spheroidal and cylindrical roughness elements. The conditions of smallness are, in terms of the spacing h and radii d of the roughness elements, kd&lt;kh?1. Of special interest, in this and in previously studied cases, has been the prediction of a boundary wave associated with the roughness and traveling along the surface at slightly subsonic speeds, the existence and properties of which have been verified experimentally in the rigid wall case [H. Medwin et al., J. Acoust. Soc. Am. 66, 1131–1134 (1979)]. The theory is basically different from other approaches to rough surfaces scattering in that the emphasis is on nonstochastic models and, more importantly, in that it incorporates nearfield dipole interactions between steep-sided scatters as well as explicit diffraction effects. The procedure is to first establish the basic small scatterer approximations for any of shape, then to sum the contributions of planar distributions of such scatterers; this leads to a simple boundary condition, of first order in kd, applied to a plane z = const. Critical in this derivation are (1) the concept of virtual mass of the scatterer (Lighthill) and (2) a condition of imbeddedness which says that, in a system of coordinates moving with the fluid, a scatterer does not move normally to the interface. The latter condition ensures that the backscatter from a small hemispherical or hemicylindrical roughness element protruding into the half-space (ρ1,c1) is equivalent to that from a whole spheroid or cylinder in a full space (ρ1,c1). These generalized boundary conditions allow one to determine directly the conditions of existence and the amplitude of the boundary wave excited by a point source of sound on or near the rough interface. Of particular interest are: (a) The case of hemicylindrical corrugations where, for d/h?0.4, boundary wave amplitudes can be substantially larger than for hemispherical bosses, at least for directions of travel normal to the corrugations; in other directions the amplitude is multiplied by a factor cos2 ψ, where ψ is the angle between the horizontal wavenumber vector and the normal to the corrugation axes. (b) The sensitivity of the boundary mode to all parameters and, in particular, to ρ1/ρ2 and c1/c2. Calculation shows that, insofar as underwater sound experiments are concerned, the boundary mode is most likely to be observed near the ocean floor, rather than near the surface. But whereas the rough sediment–water interface can support a boundary wave, its existence and amplitude depend critically on the values of the above parameters. Pebbles or nodules scattered evenly on the ocean floor should provide the best conditions for observing this mode; conversely, measurement of boundary wave amplitudes could in principle be used to measure the mean density of nodules. As suggested elsewhere [I. Tolstoy, J. Acoust. Soc. Am. 69, 1290–1298 (1981)] this effect will be especially well marked under shadow zone conditions. It may also be relevant to other fields of acoustics, such as aeroacoustics or concert hall acoustics.