Wave scattering by a periodic array of porous breakwaters

This paper studies wave scattering by a periodic array of rectangular porous rubble-mound breakwaters (bars). An analytical solution is developed based on potential flow and classical porous medium theories. In the solution procedure, the periodic boundary conditions for the velocity potential and its derivative in the direction of the breakwater length are introduced, and then the problem for the whole breakwaters is reduced as the wave scattering problem corresponding to a single porous bar. The fluid domain for a single bar is divided into multiple regions. The velocity potentials in outer regions are expressed by adopting a conventional eigenfunction expansion method, whereas the velocity potentials in middle regions are obtained using a velocity potential decomposition method. The unknown expansion coefficients in the velocity potentials are determined using the matching conditions on the boundaries between adjacent regions. The analytical solution is confirmed by examining its convergence and several limiting cases for the present breakwaters. Multi-parameter analyses are performed to clarify the reflection coefficient, transmission coefficient, energy loss coefficient, and free surface amplitude near the breakwaters. Some useful results for engineering applications are presented.