Scattering of obliquely incident water waves by a surface-piercing porous box

Abstract

We investigate the scattering of obliquely incident water waves by a surface-piercing porous box in finite depth of fluid. The physical problem is modelled based on the small amplitude water wave theory and Darcy’s law for flow past a porous structure. Using the matched eigenfunction expansion method, the boundary value problem is reduced to a system of linear algebraic equation. Further, these equations are solved numerically to compute physical quantities of interest like reflection and transmission coefficients. The assessment of the mathematical model is made through a comparison with the existing experimental and theoretical studies. As a special case, the results for wave interaction with (i) rigid box and (ii) single/ double porous barriers in the absence of submerged porous plate are compared with earlier published results available in the literature. In addition, the forces acting on the box are also evaluated. The efficiency of the proposed model in reflecting, transmitting and dissipating the wave energy is illustrated through various graphs. The study reveals that the height and width of the porous box play important roles for not only wave trapping inside the structure, but also dissipating a major part of wave energy by the structure to reduce wave transmission for creating a calm region on the lee side of the structure.