Interaction between a Solitary Wave and a Fixed Partially Submerged Body with Two Extended Porous Walls

Abstract

Approximate analytical solutions that can be applied effectively to describe the wave transformation of a solitary wave propagating past a partially submerged stationary body of rectangular shape with two attached side porous walls are introduced in this paper. Laboratory measurements of the free-surface elevation were also performed to validate the analytical predictions. The velocity potentials in the upstream and downstream of the fluid domain are formulated using the Fourier integral approach. Applying the boundary and matching conditions, including Darcy’s law–based porous wall conditions, and the concept of the orthogonality of eigenfunctions, the unknown coefficients are analytically derived. The results of free-surface elevations and hydrodynamic forces are presented. It is found that the transmitted wave profiles predicted from the present analytical model match well with the experimental data and other published numerical results, while the calculated reflected wave elevations are shown to slightly overestimate the wave peak. The physical parameters that affect the wave transformation and hydrodynamic forces on structures are investigated. With the addition of the extended porous walls, the overall reflection coefficient increases slightly for smaller amplitude waves; however, the overall transmission coefficient is reduced significantly for all wave conditions. The hydrodynamic force decreases with an increase in porous-effect parameters. An increase of the body draft or the body thickness can also enhance the reduction of the transmitted wave amplitude.