Water Wave Scattering by a Dock in Presence of Bottom Undulation

The problem of water wave scattering by a semi-infinite floating dock on the free surface of an ocean with variable bottom topography is considered using linear theory. By employing a perturbation analysis and using Green's integral theorem, the analytical expression for the first order reflection coefficient is obtained in terms of a computable integral involving the bottom shape function. Also the zero order reflection coefficient is obtained by using residue calculus method. The first order reflection coefficient is computed numerically by considering some special types of bottom shape function and is depicted graphically against the wave number in a number of figures.