Wave interaction with a submerged semicircular porous breakwater placed on a porous seabed

In the present study, a coupled eigenfunction expansion-boundary element method is developed and used to analyze the interaction of surface gravity waves with a submerged semicircular porous breakwater placed on a porous seabed in water of finite depth. Two separate cases: (a) wave scattering by the semicircular breakwater, and (b) wave trapping by the semicircular breakwater placed near a porous sloping seawall are studied. Further, as a special case, wave trapping by a semicircular breakwater placed on a rubble mound foundation near a sloping seawall is analyzed in water of uniform depth having an impermeable bed. The wave motion through the semicircular permeable arc of the breakwater is modeled using the Darcy's law of fine pore theory, whilst the wave motion through the porous seabed, rubble mound foundation and the porous seawall are modeled using the Sollitt and Cross model. The friction coefficient defined in Sollitt and Cross model is computed by approximating the spatial dependency of the seepage velocity with the average velocity within the porous media. An algorithm for determining the friction coefficient f is provided. Various physical quantities of interests are plotted and analyzed for various values of waves and structural parameters.