Novel analytical solutions without finding complex roots for oblique wave scattering by submerged porous/perforated structures. (July 2021) - Li, Ai-jun; Liu, Yong; Fang, Hui
Abstract: This study develops new analytical solutions to oblique wave scattering by submerged porous/perforated structures on the basis of linear potential theory. Two cases of a porous (rubble mound) breakwater and a horizontal perforated plate are considered. The new solutions have the novelty of using a contour integral technique to avoid finding the complex roots (wave numbers) of complex dispersion equations for water wave motion over porous/perforated structures. In the solution procedure, the linear equation systems for the expansion coefficients in velocity potentials are obtained by using the conventional mode-matching method. However, the matrix elements involving the complex wave numbers are recast by using the contour integral technique, and then the expansion coefficients are determined without knowing the explicit knowledge of complex wave numbers. As a result, the difficulties arising in solving the complex dispersion equations in the traditional solutions are avoided completely. The calculation results of the new solutions agree well with known results of analytical approaches with complex wave numbers, analytical solutions based on the velocity potential decomposition method, and numerical solutions based on the multi-domain boundary element method. This study gives a simple and elegant procedure to tackle water wave interactions with submerged porous/perforated structures, and the solutions can be used as a reliable alternative tool for fast engineering preliminary analysis.