Third-harmonic wave diffraction by a vertical cylinder

The diffraction of regular waves by a vertical circular cylinder in finite depth water is considered, within the frame of potential theory. The wave slope kA is assumed to be small so that successive boundary value problems at orders kA, k2A2, and k3A3 can be formulated. Here we focus on the third-order (k3 A3) problem but restrict ourselves to the triple-frequency component of the diffraction potential. The method of resolution is based on eigenfunction expansions and on the integral equation technique with the classical Green function expressed in cylindrical coordinates. Third-order (triple-frequency) loads are calculated and compared with experimental measurements and approximate methods based on long-wave theories.