Wave scattering by multiple floating flexible circular plates over a porous bed

Abstract

This study develops a theoretical model to analyze wave scattering between multiple floating flexible circular plates and water waves propagating over a porous bed. This boundary value problem is tackled using the eigenfunction expansion technique along with Graf’s addition theorem. Utilizing the relevant boundary conditions, the unknown velocity potentials for the outer area and the plate-covered regions are determined. In each region of the problem domain, the velocity potentials associated with the incident and scattered waves are expressed through an expansion utilizing Bessel and Hankel functions. The study incorporates three distinct edge boundary conditions: clamped, moored, and free. The effectiveness of this study in evaluating the influence of various parameters is assessed by analyzing the heave force acting on the circular plates. This study reveals a compelling trend: as the porous-effect parameter associated with the porous bottom increases, the heave force exerted on the circular plates exhibits a significant reduction. It is also observed that for an array of two, three, and four circular flexible plates, the heave force on each subsequent plate is reduced compared to the preceding plates. Furthermore, to clearly visualize the wave dynamics around the circular flexible plates over time, a time simulation of the fluid flow is provided for different porosity parameter values. This simulation shows a reduced wave amplitude in the lee-side zone. The flow distributions around the circular plates are illustrated both with and without single or multiple circular plates, indicating a lower amplitude in the lee-side zone. The porous bed significantly contributes to diminishing the wave force exerted on the circular plates and establishing a calm area on the back side of the structures.