Wave scattering by an energy island with an arc breakwater

In this paper, a theoretical model is proposed within the framework of linear potential flow theory to study the interaction of water waves with an energy island system, comprising an inner sectored basin partially enclosed by the island structure and a porous, arc-shaped breakwater. The physical properties are described by a complex spatial velocity potential, with solutions in the inner and outer fluid domains expanded into eigenfunctions and matched in the sense of a Galerkin technique. The arc breakwater's porous nature facilitates wave energy dissipation, which is analyzed via two methods: a direct approach assessing power dissipation across the breakwater's surface and an indirect method calculating energy loss through velocity potential solutions from the outer region. Wave excitation forces acting on the energy island and breakwater are evaluated, while free surface elevations within the enclosed basin and outside the island system are also investigated to examine risks associated with large wave amplification. It is found that increasing breakwater length shifts the first peak of the basin's wave-height frequency response to lower frequencies while amplifying its magnitude. This work advances the theoretical understanding of wave interactions with energy island systems, informing the design and optimization of such structures for coastal engineering applications.