Wave propagation passing over a submerged porous breakwater

A linear model of waves propagating over a submerged porous breakwater is derived from two coupled boundary-value problems, each of which represents the governing equation in a different medium. The model is similar to the shallow-water equations (SWE), with a damping term proportional to the character of the porous breakwater. Therefore, waves traveling above the breakwater will be absorbed, and the amplitude decreases. The wave propagation passing over the submerged breakwater for monochromatic and solitary waves is analyzed. For monochromatic waves, the numerical solution agrees with the analytical. The amplitude decreases exponentially with respect to the space variable in the region above the breakwater. The reflected wave is also analyzed when the model is combined with a model using the shallow-water equations.