Water wave scattering by two partially immersed nearly vertical barriers

This paper provides a mathematical investigation of the problem of scattering of surface water waves by two surface-piercing barriers that are almost vertical and are described by the same shape function in the context of linear theory by employing a simplified perturbational analysis. Green's identity is used to express the perturbation to the quantities of interest-the reflection and transmission coefficients-in terms of the solution to the unperturbed system. As in the case of single nearly vertical barrier, here also the perturbed transmission coefficient vanishes identically while the perturbed reflection coefficient is obtained in terms of a number of definite integrals involving shape function. When the two barriers are merged into a single barrier, the known result for a single barrier is recovered.