Interaction of water waves with an array of permeable horizontal submerged cylinders

Abstract

This study explores the hydrodynamic interaction of water waves with arrays of submerged horizontal permeable cylinders using Darcy's law and linear wave theory. A semi-analytical model, based on the eigenfunction expansion method, is developed to investigate wave attenuation, added mass, and damping coefficients. The developed model is validated against results from the existing literature. The analysis investigates the effects of permeability, submergence depth, and wave characteristics — including the dimensionless wavenumber ($\mathrm{Ka}$, where $K$ is the wavenumber, and $a$ denotes the cylinder radius) and porosity parameter ($G_0$). The findings demonstrate that wave attenuation is most effective at moderate permeability ($G_0=0.5$) and wavenumbers in the range $\mathrm{Ka}=0.3$ to 0.5, achieving energy dissipation levels of approximately 20 %. At higher permeability ($G_0\ge 5$), wave attenuation and damping coefficients approach zero, as the cylinders behave almost as if they were absent. The added mass decreases with increasing permeability and becomes nearly constant for $\mathrm{Ka}>1$. Notably, damping coefficients for intact cylinders are generally higher than those of permeable cylinders near the free surface, except at $\mathrm{Ka}=0.5$, where minimum damping occurs. These findings offer valuable guidance for optimizing the design of permeable marine structures, including wave dissipators, aquaculture systems, and offshore infrastructure, by tailoring permeability and geometry for enhanced performance and durability.