Water wave scattering and energy dissipation by interface-piercing porous plates

An integral equation method is developed to study the wave interaction with two symmetric permeable plates submerged in a two-layer fluid. The plates are inclined and penetrate the common interface between the layers. The existence of two different wave modes for the incident wave gives rise to two problems. Both of these are tackled by reducing them to a set of coupled hypersingular integral equations of the second kind. Unknown functions of the integral equations are the discontinuities in the potential functions across portions of the plates. These are computed numerically by employing an expansion collocation method. New results for the reflection coefficients and the amount of energy loss are presented by varying several parameters such as porosity, angle of inclination, plate-length, separation between the plates, interface position and density ratio. Known results for two symmetric vertical permeable and impermeable plates, single vertical impermeable and horizontal permeable plates are recovered from the present analysis.