Bottom topography influence on wave transformation by a porous-flexible membrane in a two-layer oblique sea

Abstract

In a two-dimensional context, the interaction between an oblique gravity wave and a partial porous-flexible membrane barrier in a two-layer fluid with an undulating bottom has been studied using linear wave theory. Two cases (a) wave scattering and (b) wave trapping by porous-flexible membrane barrier in presence of an impermeable sea-wall are discussed. The impact of surface wave, interfacial wave, and the induced energy among these by bottom undulation has been taken into consideration. An approximation technique Mild slope equation (MSE) and Fourier method along with least square approximation have been adopted as a solution technique. The solutions obtained by former methods are matched at interfaces under suitable physical conditions which reduces the problem to algebraic system of equations. This study finds that energy dissipation of surface and interfacial wave acquires an inverse pattern for a given particular gap length between barrier and free-surface. Concave upward bottom is seen to be responsible for less dissipation of surface and interfacial waves. An opposite behavior of surface and interfacial waves on the membrane deformation has been observed. The study carried out in this article holds good potential in deepening our understanding of scattering and trapping of waves by a partial porous-flexible barrier.