A new analytical solution for wave scattering by a submerged horizontal porous plate with finite thickness

Abstract

This study gives a new analytical solution for water wave scattering by a submerged horizontal porous plate breakwater with finite thickness in the context of linear potential theory. The original velocity potential is split into a symmetric part and an antisymmetric part. Each part is further written as the sum of two artificial potentials satisfying appropriate boundary conditions. All the artificial potentials are determined by the matched eigenfunction expansions. The symmetric solution is also the solution for wave reflection by a porous plate wave absorber in laboratory flume. A multi-domain boundary element method solution is developed to confirm the analytical solution. The agreement between the results calculated by the analytical solution and the boundary element method solution is excellent. Also the analytical solution is confirmed by experimental data. The new analytical solution needs no complex dispersion relations for water wave motion over porous mediums. Thus the particular difficulties due to complex dispersion relations are avoided.