Oblique wave scattering by porous breakwaters/seawalls: Novel analytical solutions based on contour integral without finding complex roots

Abstract

This article develops novel analytical solutions to oblique wave scattering by porous rubble-mound structures based on linear potential theory. The novelty of the solutions is that the usual complex root finding algorithm is avoided by applying a contour integral technique. In the solving procedure, the whole fluid domain is divided into multiple regions, and the series solution of the velocity potential in each region is obtained using the separation of variables. A linear equation system for the expansion coefficients is achieved by matching the interface conditions between adjacent regions. The matrix elements, which initially include the complex roots of complex dispersion relations, are evaluated by applying the contour integral technique. The evaluation process is free of complex roots, and thus the difficulties arising in solving the complex dispersion relations in traditional solutions are avoided. Case studies show that the series solution converge rapidly, and the calculation results of the new solutions agree well with those of previous analytical solutions with complex roots and multi-domain boundary element method (BEM) solutions. Besides providing a simple and elegant approach for analyzing the hydrodynamic performance of porous structures, the new solutions can be extended to water wave problems involving other dissipative coastal structures.