Bragg Resonance of Water Waves by Multiple Permeable Thin Barriers over Periodic Breakwaters

Abstract

In this study, the Bragg resonance of water waves scattered by multiple permeable thin barriers over a series of periodic breakwaters was solved by employing the eigenfunction matching method (EMM). The geometrical configuration was divided into multiple shelves separated by steps, on which thin permeable barriers were implemented. The solution was approximated using eigenfunctions with unknown coefficients that were considered as the amplitudes of the water waves for each shelf. The conservations of mass and momentum were then applied to form a system of linear equations, which was sequentially solved by a sparse-matrix solver. The proposed method degenerates to traditional EMM formulations if thin barriers, the permeability of the barrier, or bottom undulations are not considered. The validity of the suggested method was examined based on the results in the literature. Bragg resonances by bottom-standing, surface-piecing, and fully submerged permeable barriers over a series of periodic trapezoidal or half-cosine breakwaters were studied. In addition, the breakwater amplitudes, permeable parameters of the barriers, and incident angles of water wave scattering by different types of periodic breakwaters were discussed.