Wave Forces on a Partially Reflecting Wall by Oblique Bragg Scattering with Porous Breakwaters over Uneven Bottoms

In this study, the scattering of oblique water waves by multiple variable porous breakwaters near a partially reflecting wall over uneven bottoms are investigated using the eigenfunction matching method (EMM). In the solution procedure, the variable breakwaters and bottom profiles are sliced into shelves separated steps and the solutions on the shelves are composed of eigenfunctions with unknown coefficients representing the wave amplitudes. Using the conservations of mass and momentum as well as the condition for the partially reflecting sidewall, a system of linear equations is resulted that can be solved by a sparse-matrix solver. The proposed EMM is validated by comparing its results with those in the literature. Then, the EMM is applied for studying oblique Bragg scattering by periodic porous breakwaters near a partially reflecting wall over uneven bottoms. The constructive and destructive Bragg scattering are discussed. Numerical results suggest that the partially reflecting wall should be separated from the last breakwater by half wavelength of the periodic breakwaters to migrate the wave force on the vertical wall.