Scattering of oblique incident waves by a floating structure with a porous wall fitted on its vertical sides in the presence of a varying bottom topography

This work analyzes the wave interaction with a rigid floating structure, with porous walls fitted on its vertical sides, to mitigate the wave-induced forces acting on the floating structure. The problem is formulated in finite ocean depth with a varying and impermeable sea-bed. The small-amplitude wave theory is used to investigate this work. The water waves, after the interaction with the varying bottom and floating structure, are partially reflected. The fluid domain is split into nine regions, and the boundary value problems associated with eight of them are solved by utilizing the methods of separation of variables and eigenfunction expansion, whereas modified mild-slope equation is used for the other region, which has a sloping bed. After obtaining the scattered potential in every region, a system of equations is obtained using the continuity of pressure and mass flux. The roots of the dispersion relation are analyzed, calculated, and incorporated into the system of equations. The energy identity relation is obtained which depicts the dissipation of wave energy. The unknown coefficients of the velocity potentials are determined, and then, the horizontal force and vertical force acting on the floating structure are evaluated. To examine the impact of the porous walls, various graphs are plotted to illustrate the reflection coefficient, transmission coefficient, and wave-induced forces on the floating structure. It is noted that, as the friction factor of the porous walls increases, the reflection coefficient decreases. It is observed that, by increasing the draft and thickness of the porous wall, reflection and transmission coefficients decrease. It is also observed that both reflection and transmission coefficients decrease when the sea-bed slope is milder compared to steeper slope. The horizontal and vertical forces on the floating structures are reduced when the sea-bed bottom is milder. The graphs of both forces show that the differences in force values are not significant for steeper and milder sea-bed slopes. In the presence of a varying bottom, both horizontal and vertical forces acting on the floating structure are reduced compared to those on a flat bottom. In order that the proposed model is useful for engineering applications, rough ranges of values of some parameters are proposed. The validity of the proposed model is established by comparing it against two available models. Furthermore, a comparison of the present model with another model points toward the efficiency of the present model.