Scattering of surface waves by a pair of asymmetric thin elliptic arc shaped plates with variable permeability

Abstract

Abstract We consider the interaction between incident surface water waves and two asymmetric curved porous plates which assume the shape of ellipse. The permeability of the plates is not uniform. This is assumed to vary along the circumference of the elliptical arc. Two coupled integral equations are derived for the problem and are solved by employing an appropriate algorithm. Using these solutions, the numerical estimates for the reflection and the transmission coefficients, amplitudes of the hydrodynamic forces and energy dissipation coefficient are computed. The accuracy of the numerical results is established through an energy identity valid for permeable plates, and by comparing them with the published ones. A selection of new results is also presented for illustrative purposes. Importantly, in the present paper a mathematical method is developed to solve the problem of wave interaction with non-vertical (elliptic) plates with variable permeability. The derived numerical results indicate that the system of dual elliptic plates serves as a suitable model for a wave lens.