Scattering from a sinusoidal ocean surface excited by an underwater acoustic line source

The scattering of underwater acoustic waves from a rough ocean surface has been of interest for many years. Most theoretical approaches to the problem use the Helmholtz integral formulation, which requires many approximations to reach simple formulas. In most other approaches to the problem, the acoustic source is considered to have a small beam angle, or plane wave front, which neglects any direct path from the source to the observer. However, certain situations arise particularly in underwater acoustic ranges where the direct path is also important. The purpose of this paper is to determine the farfield produced by an acoustic line source located below a sinusoidal ocean surface. Certain situations arise where the sinusoidal model is a good approximation of an actual ocean surface. For this case, the amplitude of the sinusoidal surface is small compared with the acoustic wavelength in the ocean medium; therefore, a Fourier integral-perturbation series approach can be used to solve the boundary value problem. The resulting acoustic field is composed of the incident and specularly reflected field from a flat surface plus a scattered term for the sinusoidal roughness. The magnitude of the scattered term is directly proportional to the sinusoidal surface amplitude in wavelengths and scattering occurs for specific wavenumber relationships. Graphs are presented of the field variation as a function of the sinusoidal ocean wave motion. Although the scatter theory was applied to a sinusoidal surface, it can be shown that the theory can be applied to any surface that is Fourier transformable.