Effects of vertical porous barrier on progressive waves in a two layered fluid

Two dimensional scattering of linear water wave by thin vertical permeable plate in a two-layer fluid with free surface is considered. The permeable barrier is completely submerged in the upper layer of finite depth over a layer whose depth is either infinite or finite. For discontinuity in the potential across the plate, we use Green's integral theorem to formulate the problem in terms of a hypersingular integral equation. A collocation method using a finite series of Chebyshev polynomials of second kind have been introduced to get the unknown difference potential numerically. The reflection and transmission coefficients for surface and internal modes are computed as an integral involving difference potentials. The proportion of reflected and transmitted energies of both the wavenumbers are calculated. Moreover, amount of energy dissipated due to the presence of permeable plate in the upper layer are obtained. Numerical results are calculated and depicted graphically against the wavenumber for various non-dimensionalized parameters.