Scattering of gravity waves by a circular dock

Abstract

The scattering of a gravity wave of wave number k by a circular dock of radius a and draft d – h in water of depth d is calculated through a variational approximation. The total and differential scattering cross-sections, the peripheral displacement, and the lateral force on the dock are presented as functions of ka with d/a and h/d as parameters and compared with the classical results for a circular cylinder (h = 0). A pronounced resonance is found near ka = 2 for certain values of d/a and h/d.