Surface gravity wave interaction with a submerged horizontal flexible porous plate

An analytical study for surface gravity wave interaction with submerged flexible porous plate based on small amplitude water wave theory and structural response is presented. The flexible porous plate is modeled based on the thin elastic plate theory and wave past porous plate is using generalized Darcy's law to incorporate both frictional force and inertia force. The dispersion relation is analyzed to determine the wave motion characteristics of two propagating wave modes in the presence of free surface and flexural waves at the submerged horizontal porous plate in specific cases. Further, the linearized long wave equation under shallow water approximation is derived in a direct manner and the limiting cases are compared. The integral forms of Green's functions are derived using the fundamental solution associated with the two-dimensional Laplace equation. Using Green's identity, the generalized expansion formulae for the wave-maker problem associated with the surface wave interaction with the submerged flexible porous plate are obtained in both the cases of finite and infinite water depths. The usefulness of the expansion formula is demonstrated by analyzing a physical problem associated with the surface gravity wave interaction with a moored finite submerged horizontal elastic porous plate in finite water depth. In the numerical results, the accuracy of the numerical computations are checked and the combined effect of mooring stiffness and porous-effect parameter are analyzed on the reflection coefficients, wave energy dissipation coefficients, and vertical forces. It is observed that the wave energy dissipation/absorption depends significantly on the mooring stiffness, porous-effect parameter, and suitable positing of the submerged plate.