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In this paper the interaction of a two-dimensional progressive wave train over a submerged rectangular porous breakwater is studied theoretically. For this purpose, the time dependent incompressible Navier-Stokes-Brinkman system is newly derived for wave propagating over submerged breakwater. A staggered grid Finite Volume Method (FVM) is used to solve the Navier-Stokes-Brinkman system. The free surface boundary condition and the interfacial boundary conditions between the water and porous media are in complete form. A Volume-of-Fluid (VOF) methodology is employed to track the free surface. The validity of present model is verified based on the compressions with the existing experimental results. Having verified the accuracy of the numerical model, the effects of several parameters of a wave and a submerged breakwater were systematically investigated. The results indicate that the wave transformations are affected primarily by the breakwater width and the structure permeability. The numerical results also illustrate that for the porous breakwater, an optimum porosity value seems to exist at which the transmitted wave height is minimized. It has been observed that the transmission coefficient decreases as the permeability increases. However, the results indicate that further increase of the structure permeability beyond the optimal value increase the transmission coefficient

Navier-Stokes-Brinkman system for interaction of viscous waves with a submerged porous structure