Effect of thin vertical porous barrier with variable permeability on an obliquely incident wave train

Abstract

The present paper is concerned with a study of wave propagation due to incidence of an obliquely incident wave on a thin porous vertical barrier with variable porosity. Two different configurations of the barrier are considered: 1. partially immersed barrier 2. bottom standing barrier in water of finite depth. The problem is formulated in terms of a Fredholm integral equation of the second kind, where the unknown function represents the difference of potentials across the barrier. The integral equation is then solved using two methods: the boundary element method and the collocation method. Using the solution of the integral equation, the reflection coefficient and amount of energy dissipated are determined and depicted graphically. It is observed that a barrier with variable porosity induces more reflection than a barrier with constant porosity. Also the energy dissipation for barrier with variable porosity is in general less than a barrier with constant porosity. However for partially immersed long barrier, energy dissipation of waves with certain wavelength is more for barrier with variable porosity than a barrier with constant porosity. For both configurations of the barrier, a long barrier induces more reflection and dissipation of wave energy. The inertial force coefficient of the porous material of the barrier reduces the reflection and dissipation of wave energy. Also, for an obliquely incident wave, the presence of porous barrier reduces reflection and dissipation of energy as compared to a normally incident wave.