Scattering of water waves by dual asymmetric vertical flexible porous plates

Abstract

In this article, we focus on investigating the problem of water wave scattering by dual asymmetric vertical flexible porous plates submerged at different depths within the framework of two-dimensional linear potential theory. Employing Havelock's theorems for water wave potential and using the plate boundary conditions the problem is reduced to a pair of coupled hypersingular integral equations. Numerical solutions to the integral equations are determined by using polynomial approximations to the unknown functions together with a technique to tackle the hypersingular integral part and finally by collocating at finite number of points. The energy balance relation for the present scattering problem involving two flexible porous plates is obtained using Havelock's theorem. The present method is verified by comparing the numerical results for limiting cases with the known results available in the literature and through the energy balance relation. Also, a number of selective results for the reflection coefficient, the energy loss coefficient and the hydrodynamic forces on the plates are presented graphically. It is observed that a proper arrangement of the dual plates may dissipate sufficient amount of wave energy thereby providing an efficient model of breakwater.