Surface wave scattering by porous and flexible barrier over a permeable bed

Abstract

Using small amplitude wave theory, scattering of water waves by a vertical flexible barrier over a porous bed is studied. The boundary value problem in the form of Helmholtz equation is solved by the matched vertical eigenfunction expansion method. By exploiting the continuity of pressure and velocity at the interface along with Darcy's law for porous structure, the obtained coupled relation is solved by least-squares approximation method. The behavior of flexible barrier against the wave action for various physical quantities are studied and the numerical results are discussed. It is observed that due to the porous structure, a tranquility zone is created on the lee side of the barrier.