A numerical wave model is developed to simulate wave transformation in the surf zone. The governing equation is the parabolic formulation of the mild-slope equation including wave breaking and energy dissipation over porous media. Following Mordane et al. (2004) the present theory is obtained by splitting the Berkhoff's equation operator into two parabolic operators representing progressive and reflected wave propagation, respectively. The use of the Padé [2,2] approximation permits to derive the parabolic equation for transmitted waves and to model wave propagation at very wide propagation angles over a porous bed. The model is verified through experiments for waves propagating over a uniform and composite uniform impermeable slope and waves passing over submerged permeable breakwaters with porosities. The parabolic model is also used for the case of wave propagation at large angle incidence over a porous elliptic shoal. Energy dissipation due to wave breaking has been accounted for in the computations. Numerical results are in good agreement with experimental results.
The porous structures, such as seawalls, detached breakwaters or submerged breakwaters, are frequently used to protect coastal erosion from wave attack. The effectiveness of these structures is owing to that they are able to reflect and absorb wave energy and to dissipate it by wave breaking on the structures. Wave energy reduction on the lee side of the porous structures increases so that only a small part of the wave energy is transmitted to onshore. Consequently, the wave field in the lee side of the structures becomes quiet and the intensity of the wave action on the shoreline decreases, and the migration of coastal erosion and its corresponding coastal disasters can be protected. The knowledge of wave transformation over porous media is required to determine the stability of the porous media and to evaluate the effectiveness of wave energy reduction of the structures.
