Reflected wave energy by two collinear submerged wavy breakwaters

Under the assumption of a potential flow, we obtain an asymptotic solution up to the second order in a regular expansion, for the problem of the interaction between linear long waves and two submerged floating breakwaters of wavy surfaces, placed in a collinear manner. The hydrodynamics that results from the interaction between the waves and the structures is modeled with the aid of the well-known shallow water wave equations together with the Laplace equation. For this purpose, the domain perturbation method is used to obtain the solution of the governing equations and assume, as is common, small amplitudes of the breakwater's wavy surfaces. This solution is compared with classical analytical solutions reported in the specialized literature, and they adjust properly. Several geometrical configurations of the breakwaters are analyzed. As the breakwaters are near the free surface elevation, just at one-third of the total water depth, larger values of the reflection coefficients are obtained. The maximum wave reflection occurs for four undulations of the breakwater surfaces. In addition, the wave reflection increases as the amplitude of the surfaces of the breakwaters increases. The results of this study are expected to be used by coastal engineers for preliminary feasibility and desk design of submerged breakwaters with wavy surfaces.