Scattering of Surface Waves on an Infinitely Deep Fluid

Abstract

The reflection and transmission of small amplitude waves incident on a plane barrier submerged in an infinitely deep fluid are investigated; the barrier has a finite width and is parallel to the undisturbed free surface of the fluid. Green's function techniques are used to represent the velocity potential in terms of its discontinuity (pressure difference) across the barrier. The application of the boundary condition at the barrier leads to a one-dimensional integral equation for the pressure difference. This equation is extended by introducing the fluid velocity normal to the plane of the barrier, and then it is analyzed by the complex Fourier transform methods of Wiener and Hopf. The velocity transforms are found to be characterized by a pair of dual inhomogeneous integral equations which allow systematic approximation by iteration. A convolution provides representations for the velocity potential in the different regions of the fluid, and these are the basis for investigating the reflection and transmission of waves. Results for some related problems (e.g., scattering by a semi-infinite barrier, by a finite dock, etc.) are obtained as limiting cases.