Iterative analytical solution for wave reflection by a multi-chamber partially perforated caisson breakwater

Abstract

This study examines wave reflection by a multi-chamber partially perforated caisson breakwater based on potential theory. A quadratic pressure drop boundary condition at perforated walls is adopted, which can well consider the effect of wave height on the wave dissipation by perforated walls. The matched eigenfunction expansions with iterative calculations are applied to develop an analytical solution for the present problem. The convergences of both the iterative calculations and the series solution itself are confirmed to be satisfactory. The calculation results of the present analytical solution are in excellent agreement with the numerical results of a multi-domain boundary element solution. Also, the predictions by the present solution are in reasonable agreement with experimental data in literature. Major factors that affect the reflection coefficient of the perforated caisson breakwater are examined by calculation examples. The analysis results show that the multi-chamber perforated caisson breakwater has a better wave energy dissipation function (lower reflection coefficient) than the single-chamber type over a broad range of wave frequency and may perform better if the perforated walls have larger porosities. When the porosities of the perforated walls decrease along the incident wave direction, the perforated caisson breakwater can achieve a lower reflection coefficient. The present analytical solution is simple and reliable, and it can be used as an efficient tool for analyzing the hydrodynamic performance of perforated breakwaters in preliminary engineering design.