Water wave scattering by two vertical porous barriers over a rectangular trench

This paper provides a semi analytical technique to handle the problem of water wave scattering by thin vertical double porous barriers over rectangular trench assuming linear theory. The motivational theme behind this study is the exploration of a novel representation of a breakwater model in the history of water wave theory. Specifically, the study focuses on the wave scattering problem of a pair of thin porous barriers, along with a rectangular trench, incorporating integral equations that encompass both types (half and one-third) of singularities. The problem is put together in terms of integral equations by presuming symmetric and anti-symmetric parts of velocity potential. Using multi-term Galerkin method in terms of Chebychev polynomial and ultra-spherical Gegenbauer polynomial as its basis function due to the edge conditions at the submerged end of the barrier and at the corner of the trench, respectively, to figure out the analytical solutions. The approach of this study also provides a technique for solving a system of integral equations that accommodates various singularities at the corners of the trench (cube root singularities) and submerged edges of the thin porous barriers (square root singularities). The reflection and transmission coefficients, dissipation of wave energy and dynamic wave force are obtained for different parametric values which are depicted graphically against the wave number. It is reliable that the length and position of porous barrier execute a major impact in the reflection and transmission coefficients of surface wave.