Wave interactions with a cylinder surrounded by an arc-shaped breakwater

Inspired by the energy island used for energy storage, conversion, and transmission, this study explores the water wave interactions with a bottom-standing cylinder surrounded by an arc-shaped breakwater of negligible thickness. The arc-shaped breakwater can be either impermeable or porous. To analyze the problem, a semi-analytical matched eigenfunction expansion method is developed within the framework of linear potential flow theory. The fluid domain is divided into subdomains, with the velocity potentials in each subdomain expressed as eigenfunction expansions. Matching conditions, ensuring continuity in pressure and normal velocity, are imposed at the juncture boundary. The accuracy of the developed semi-analytical method is verified through comparison with results obtained using the numerically-based boundary element method. Extensive discussions are made on hydrodynamic responses, including wave exciting force and free surface elevations. When the breakwater is impermeable, fluid resonance occurs in the gap between the cylinder and the arc-shaped breakwater, leading to significantly large responses in both free surface elevation and hydrodynamic forces. A simple method is developed to estimate the resonant frequencies and mode shapes associated with these resonances. On the other hand, it is observed that the presence of the porous breakwater considerably reduces the free surface responses in the gap as well as the hydrodynamic loads on the cylinder. The porous breakwater effectively mitigates the occurrence of fluid resonance and offers an efficient means to dampen wave energy, providing valuable insights for wave energy dissipation and coastal engineering applications.