The finite dock problem

The scattering of water waves by a dock of finite width and infinite length in water of finite depth is solved using the modified residue calculus technique. The problem is formulated for obliquely incident waves and the case of normal incidence is recovered by taking an appropriate limit. Exciting forces and pitching moments are calculated as well as reflection and transmission coefficients. The method presented in this paper takes account of the known solution for the scattering by a semi-infinite dock to produce new and extremely accurate approximations for the reflection and transmission coefficients as well as a highly efficient numerical procedure for the solution to the full linear problem.