Wave attenuation by multiple thin vertical porous walls in water of uniform finite depth

Abstract

The analysis for wave attenuation by multiple thin porous walls submerged in water of uniform finite depth is carried out under the acceptance of linear theory of water waves. Two different types of barrier configurations are considered, namely partially immersed walls and bottom-standing walls. A set of coupled Fredholm-type integral equations are obtained for the boundary value problem by employing Havelock's inversion formulae and continuity of water wave potential across the gap below or above the walls. The methodology adopted to solve these integral equations is multi-term Galerkin's approximation with Chebychev's polynomials as a set of basis functions multiplied by suitable weights. Also, the square-root singularity of fluid velocity at the edge of the porous walls is precisely handled. The numerical results are depicted for reflection and transmission coefficients, dissipation of wave energy and dynamic wave force against wavenumber for different parametric values involving in the barrier configurations. This theory demonstrates that the dynamic wave forces exerted on the porous walls are reduced significantly as the magnitude of the porous effect parameter is increased. The present study is ratified with the existing results in the literature of water waves for a single as well as double rigid barriers and single porous barrier.