Step approximation on oblique water wave scattering and breaking by variable porous breakwaters over uneven bottoms

In this study, the scattering of oblique water surface gravity waves by variable porous breakwaters over uneven bottoms is investigated using the eigenfunction matching method (EMM). In the EMM procedure, the variable breakwaters and bottom profiles were sliced into shelves separated by steps. The solutions on the shelves are composed of eigenfunctions. Then, by applying the conservations of mass and momentum, a system of linear equations is obtained and can be solved with a sparse-matrix solver. The effects of wave breaking and dissipation were also included in the EMM formulation using energy-dissipation factors. In order to validate the proposed EMM method, the numerical solutions were compared with the results in the literatures for non-breaking wave scattering by rectangular and parabolic porous breakwaters. The convergence of the proposed solutions was studied. Then some discussions were provided when the EMM with energy-dissipation factors was applied to evaluate the surface elevations of breaking and/or dissipated waves. The numerical results illustrated the potential application of the EMM for problems with wave breaking and dissipation if the empirical formulas for the energy-dissipation factors can be well calibrated in future researches. Some further applications were provided, including wave scattering by multiple porous breakwaters.