Three‐Dimensional Scattering of Solitary Waves by Vertical Cylinder

Abstract

This is a study of the scattering and diffraction of a solitary wave by a surface‐piercing vertical cylinder held fixed in shallow water. Particular interest is focused on the roles played by the nonlinear effects and the dispersive effects in this fully three‐dimensional problem of strong interaction between a solitary wave and a solid structure. The theoretical model adopted here for predicting the scattering and propagation of three‐dimensional long waves in shallow water is the generalized Boussinesq (gB) two‐equation model, developed by Wu. Using this model, the predicted flow field, the free‐surface elevations, the wave‐induced forces acting on the cylinder during the wave impact, and the subsequent evolution of the scattered wave field are numerically evaluated. The numerical results show that the front of the scattered wave field propagates very nearly in a circular belt, which is concentric to the cylinder as an overall topographical structure. This remarkable asymptotic geometrical feature of the resulting scattered wave cannot be obtained without the basic equations being able to correctly model the three‐dimensional effects, and without bias toward the direction of wave propagation. The role of the nonlinear, dispersive, and linear wave effects during the wave‐structure interaction are discussed in detail.