Wave attenuation by a floating breakwater of permeable submerged cylinders: A semi-analytical approach

This study presents a significant extension of the hydrodynamic model for wave interaction with arrays of submerged, permeable horizontal cylinders. Moving beyond the limitation of uniform immersion depth [Gharechae et al., “Interaction of water waves with an array of permeable horizontal submerged cylinders,” Eur. J. Mech.-B 114, 204353 (2025)], we develop a robust semi-analytical model based on Darcy's law and eigenfunction expansion to analyze a floating breakwater where cylinders can be positioned at varying, non-uniform submergence depths. The model is validated against established literature. A comprehensive parametric study investigates the influence of permeability (G0), submergence depth (h), cylinder arrangement, and wavenumber (Ka) on wave attenuation, excitation forces, and hydrodynamic coefficients. The results demonstrate that this flexible configuration enables enhanced design optimization. A key finding is that Arrangement “A” (upright triangle, with more cylinders near the surface) consistently outperforms Arrangement “B” (inverted triangle) in the critical low-wavenumber regime (Ka<0.6), achieving up to 94.3% wave energy attenuation at Ka=0.4 with moderate permeability (G0=0.5). Crucially, introducing permeability provides a dual benefit: it not only boosts energy dissipation but also significantly reduces wave excitation forces by up to 50%, easing structural and mooring design demands. Optimal performance is shown to be highly dependent on the specific combination of geometric and hydrodynamic parameters. The findings provide a solid basis for guiding the optimized design of efficient and adaptable permeable marine structures for coastal protection.