Scattering of Gravity Waves by Multiple Submerged Rubble-Mound Breakwaters

Abstract

A numerical model based on multi-domain is developed to investigate the scattering of surface gravity waves by an array of submerged rubble-mound breakwaters. The boundary value problem is analysed in two dimensions under the assumption of small-amplitude wave theory in the water of finite depth. Analytical solution based on the eigenfunction expansion method is independently developed to validate the numerical model in addition to available results in the literature. Various configurations such as trapezoidal, triangular, and circular shapes are investigated parametrically. The performance characteristics are discussed by analysing the scattering coefficients (such as reflection, transmission, and damping coefficient) for different physical parameters like relative water depth, relative structural dimensions, relative spacing, and the number of submerged breakwaters. In the case of trapezoidal breakwaters, the crest width plays a major role in dampening the wave energy by a whopping 90%. Moreover, the wave damping performance of triangular breakwaters is very poor. The Bragg resonant reflection is observed to be a trivariate function, which depends on structural porosity, structural thickness, and the number of submerged breakwaters. The free spacing is evident in adjusting the position of Bragg resonant reflection by multiple equi-spaced structures of several shapes. The present study will be useful in the effective design of Bragg breakwaters for establishing a calm wave environment near the harbour regions.