Scattering of linear gravity-capillary waves by a completely submerged vertical porous elastic plate

Abstract

The problem of water wave scattering by a vertical porous elastic plate completely submerged in water of infinite depth in the presence of surface tension at the free surface is investigated. Using the concepts of linear water wave theory and Green's Integral theorem, a second kind Fredholm integral equation is obtained which is hypersingular in nature. The obtained hypersingular integral equation is solved numerically. A new mathematical form of the energy identity has been derived which involves an energy loss term that occurs due to the combined effects of surface tension and porous nature of the plate. Numerical estimates for physical quantities like reflection coefficient, energy loss coefficient, hydrodynamic force, and plate deflection are evaluated and then depicted graphically for a certain set of parametric values. The present methodology is validated using the energy identity and the results present in the existing literature. The effect of surface tension on the propagation of gravity waves is analyzed with the help of the various hydrodynamic quantities, which portrays that it is not always insignificant.