Waves propagating over a two-layer porous barrier on a seabed

A research of wave propagation over a two-layer porous barrier, each layer of which is with different values of porosity and friction, is conducted with a theoretical model in the frame of linear potential flow theory. The model is more appropriate when the seabed consists of two different properties, such as rocks and breakwaters. It is assumed that the fluid is inviscid and incompressible and the motion is irrotational. The wave numbers in the porous region are complex ones, which are related to the decaying and propagating behaviors of wave modes. With the aid of the eigenfunction expansions, a new inner product of the eigenfunctions in the two-layer porous region is proposed to simplify the calculation. The eigenfunctions, under this new definition, possess the orthogonality from which the expansion coefficients can be easily deduced. Selecting the optimum truncation of the series, we derive a closed system of simultaneous linear equations for the same number of the unknown reflection and transmission coefficients. The effects of several physical parameters, including the porosity, friction, width, and depth of the porous barrier, on the dispersion relation, reflection and transmission coefficients are discussed in detail through the graphical representations of the solutions. It is concluded that these parameters have certain impacts on the reflection and transmission energy.