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.

在线性水波理论和小振幅表面波的假设下，研究了由于存在垂直漂浮的刚性圆柱体而导致的可渗透海床上的波浪色散。使用辐射条件和边界条件，确定自由表面区域和圆柱体覆盖区域的未知电势。使用问题中每个区域的贝塞尔和汉克尔函数来扩展入射波和散射波的速度势。采用特征函数展开技术来解决由此产生的边值问题。通过演示圆柱体上的波浪力和流量分布以及不同参数下流量的时间模拟，可以验证该研究的有效性。结果表明，多孔海床上浮动圆柱体的存在显着降低了结构背风侧表面波的振幅。还表明，圆柱体的半径和高度在减少圆柱体上的波浪力方面发挥着重要作用，从而在结构的背风侧形成平静区域。拟议的设置有可能帮助设计海上结构，这些结构能够减少波浪力对沿海结构的影响，然后可以安全地用于各种海上作业。