Wave Response to a Non-uniform Porous Vertical Plate

Abstract

This paper is concerned with a study of wave propagation due to scattering of an obliquely incident wave by a porous vertical plate with non-uniform porosity which is completely submerged in water of finite depth. The problem is formulated in terms of a Fredholm integral equation of the second kind in difference in potential across the barrier. The integral equation is then solved using two methods: the boundary element method and the collocation method. The reflection coefficients, transmission coefficient, and amount of energy dissipation are evaluated using the solution of the integral equation. It is observed that non-uniform porosity of a barrier has significant effect on the reflection of waves and energy dissipation compared to a barrier with uniform porosity. The dissipation of the wave energy by a non-uniform porous barrier can be enhanced and can be made larger than that of a barrier with uniform porosity, by suitable choice of non-uniform porosity distribution in the barrier. This has an important bearing on reducing the wave power and thereby protecting the shore line from coastal erosion. Also, an obliquely incident wave reduces reflection and dissipation while increasing transmission of wave energy as compared to a normally incident wave.

Keywords

Vertical plate / Oblique incidence / Finite depth / Non-uniform porosity / Reflection coefficient / Transmission coefficient / Energy dissipation