Semi-analytical solution of cnoidal wave diffraction around a double-layer arc-shaped vertical porous breakwater

The interaction between the first-order cnoidal wave and a concentric structure with dual-arc porous breakwaters is studied semi-analytically based on eigenfunction expansion. Both arcs of the breakwater are considered as thin shell structures and rigidly mounted on a flat sea bottom. The fluid domain is divided into an unbounded and two bounded sub-domains, within which the solutions are described by eigenfunctions. Matched conditions along the boundaries between different regions are applied, leading to a semi-analytical solution of the considered problem. The method is applied to study a special case of cnoidal wave diffraction with a solid cylinder and the results of wave loads and wave runups agree excellently with reference results in the literature. For a double-layer arc-shaped vertical porous breakwater standing in shallow-water waves where cnoidal wave theory is applicable, our results show that the approach using linear Airy waves may significantly underestimate the wave loads on the breakwater. It is also shown that the dual-arc breakwater has a better protective performance than a single-arc breakwater. Parametric studies on porosity, annular spacing, opening angle, water depth and incident wave angle are also presented.