Effect of Porosity on Wave Scattering by a Vertical Porous Barrier over a Rectangular Trench

Abstract

The effect of porosity on surface wave scattering by a vertical porous barrier over a rectangular trench is studied here under the assumption of linearized theory of water waves. The fluid region is divided into four subregions depending on the position of the barrier and the trench. Using the Havelock’s expansion of water wave potential in different regions along with suitable matching conditions at the interface of different regions, the problem is formulated in terms of three integral equations. Considering the edge conditions at the submerged end of the barrier and at the edges of the trench, these integral equations are solved using multi-term Galerkin approximation technique taking orthogonal Chebyshev’s polynomials and ultra-spherical Gegenbauer polynomial as its basis function and also simple polynomial as basis function. Using the solutions of the integral equations, the reflection coefficient, transmission coefficient, energy dissipation coefficient and horizontal wave force are determined and depicted graphically. It was observed that the rate of convergence of the Galerkin method in computing the reflection coefficient, considering special functions as basis function is more than the simple polynomial as basis function. The change of porous parameter of the barrier and variation of trench width and height significantly contribute to the change in the scattering coefficients and the hydrodynamic force. The present results are likely to play a crucial role in the analysis of surface wave propagation in oceans involving porous barrier over submarine trench.

Keywords

Water wave scattering / Rectangular trench / Vertical porous barriers / Havelock’s inversion formula / Multi-term galerkin approximation / Reflection and transmission coefficients / Energy dissipation / Hydrodynamic force