Scattering of sound waves at a periodic, pressure-release surface: An exact solution

Abstract

It has been demonstrated that the problem of plane-wave scattering from a traveling ocean wave can be reduced to that of plane-wave scattering from a stationary, periodic, pressure-release surface. An exact method of solution to the latter problem is presented herein. The important characteristic of a periodic surface is that it produces strong, directional scattering when its period is comparable with the wavelength of the incident radiation, and the method provides an efficient scheme for numerical evaluation of the scattering amplitudes in case of a smooth profile of arbitrary shape. A review of previously reported ’’exact’’ solutions is given and it is shown that they fail for rather fundamental reasons which do not appear to be generally understood or appreciated. On the other hand, the work of Urusovskii on a closely related problem does not suffer from the same inadequacy and provides the lead to the rigorous method of solution given herein. It is shown how the method of solution can be extended (following Urusovskii) to treat the case of an arbitrary incident field and a refractive medium when the surface is at rest.