Scattering of Capillary Waves In Front of A Semi-Infinite Dock In An Ocean With Porous Undulatory Bottom

Abstract- The problem of scattering of capillary waves by a semi-infinite dock with a porous undulatory sea bed is attempted using perturbation technique. Two different eigen function expansions of the velocity potential function on the two sides of the surface discontinuity are constructed. An integral expression for first order reflection coefficient is arrived at involving the bottom shape function. The first order reflection co-efficient is graphically depicted in case of a sinusoidal bottom topography for various values of the porous parameter and selected values of the surface tension parameter.