Impact of Two Vertical Porous Barriers in Reflection of Water Waves and Mitigation of Wave Forces on a Rigid Floating Structure with Consideration of Uniform Current Over a Porous Sea-Bed

Abstract

This work examines an oblique water wave scattering by a rigid floating structure with the consideration of uniform current and no current, in the presence of two porous barriers with distinct height and porous properties placed in front of the structure. The objective is to study the associated reflection and to find means to mitigate the waveload on the floating structure. These barriers are considered at some distance apart from each other. It is assumed that the train of water waves interacts with the porous barriers and the floating structure due to which it undergoes partial reflection. The fluid domain is considered in terms of five distinct sub-regions in each of which the solution of the relevant boundary value problem in terms of the velocity potential is obtained through the employment of the techniques of separation of variables and eigenfunction expansion. The resulting system of equations is obtained by utilizing the matching conditions corresponding to the continuity of mass flux and pressure across each virtual vertical boundary. The roots of the dispersion relation are evaluated and utilized while solving the system of linear equations through a standard matrix technique which gives the unknown coefficients. For understanding the role of the porous barriers, the reflection coefficient and the hydrodynamic forces are evaluated and analyzed. In this context, the impact of the space between these two porous barriers, their height, and the values of the porous-effect parameters are thoroughly examined. It is observed that placing of these barriers at an appropriate distance from each other can substantially mitigate both horizontal force and vertical force acting on the floating structure. This study reveals a periodic nature of the reflection coefficient corresponding to an increase in the distance between the barriers. Further, another important observation is that the reflection coefficient results in an increment as the height of these porous barriers is increased. It, as a result, produces a reduction of the wave forces acting on the floating structure. The study of the oblique wave scattering by the floating structure is extended to the case of the presence of a uniform current. In this case, an enhancement in the reflection coefficient is observed, and subsequently, horizontal and vertical forces on the floating structure decrease. The impact of some other parameters on the reflection coefficient and the forces is also studied, and some observations are recorded. The results are validated against two established results which shows a very close match.