Interaction between long water waves and two fixed submerged breakwaters of wavy surfaces

In this work, we carried out an asymptotic analysis, up to the second order in a regular expansion, of the interaction between linear long waves and two submerged breakwaters of wavy surfaces, which obey a sinusoidal profile. The governing equations are expressed in their dimensionless version. The boundary conditions at the breakwaters surfaces are non-homogeneous; therefore, they are linearized using the domain perturbation method. Breakwaters with wavy surfaces generate larger reflection coefficient values than those obtained for breakwaters with flat surfaces. The largest values of this coefficient are obtained when the breakwater's length is of the same order of magnitude as the wavelength. The asymptotic solution is compared with classical analytical solutions and the results are in good agreement. The present asymptotic solution can be used as a practical reference for the selection of the geometric configuration of a submerged floating breakwater under shallow flow conditions.