Wave scattering by a circular cylinder over a porous bed

The dispersion of waves over a permeable seabed due to the presence of a vertically floating rigid circular cylinder is investigated under the assumptions of the linearized water wave theory and small-amplitude surface waves. Using the radiation condition and boundary conditions, the unknown potentials for the free-surface region and for the region covered by the cylinder are determined. The velocity potentials of the incident and scattered waves are expanded using the Bessel and Hankel functions for each region in the problem. The eigenfunction expansion technique is employed to solve the resulting boundary value problem. The effectiveness of the study is accessed by demonstrating the wave forces on the circular cylinder and the flow distribution along with the temporal simulation of the flow for different parameters. It is shown that the presence of a floating circular cylinder over the porous seabed reduces the amplitude of a surface wave on the leeside of the structure significantly. It is also illustrated that the radius and height of the cylinder play a significant role in reducing the wave forces on the cylinder and, hence, in creating a calm region in the leeside of the structure. The proposed setup has the potential to help design offshore structures that are capable of reducing the impact of the wave forces on the coastal structures, which can then safely be used for various marine operations.