Wave scattering by a slotted arc-shaped breakwater consisting of closely spaced piles with different cross sections

This study investigated wave scattering by a slotted, arc-shaped breakwater (SAB) consisting of an array of closely spaced piles, considering energy dissipation arising from the formation of vortices between adjacent piles. The far-field solution, valid in the region away from the SAB, is derived using a matched eigenfunction expansion method based on potential theory, where the boundary-value problem includes a porous boundary condition that incorporates energy dissipation determined by the near-field solution. The near-field solution is obtained by resolving two-dimensional viscous channel flow with varying pile cross sections (circle, rectangle, and diamond) using the computational fluid dynamics (CFD) software StarCCM+. Through systematic simulations, the empirical formula of the drag coefficient is established as a function of pile geometry and porosity. Numerical results reveal that the diamond shape among them causes more energy dissipation due to the formation of stronger vortices. By incorporating the near-field CFD-derived dissipation, including turbulent eddies, into the far-field solution, the present model effectively predicts wave deformation around the slotted, arc-shaped breakwater and identifies an optimal porosity of 0.05, achieving both effective wave attenuation and reduction of wave force. This approach of integrating potential and viscous theories by leveraging the inherent strengths of both provides an efficient design tool for assessing the hydrodynamic performance of slotted, arc-shaped breakwater configurations with varied pile geometries and porosities, enabling optimized wave-attenuation performance.