Comparison of analytical and numerical solutions for wave interaction with a vertical porous barrier

Abstract

Analytical solutions for wave interaction with a vertical porous barrier are presented. The analytical solutions are derived using two different methods for taking the depth-average of the pressure drop across the porous barrier. Both solutions assume that the evanescent modes in the wave field can be neglected. The results from the analytical models are compared to results from an iterative boundary element method (BEM) model. The BEM model shows that neglecting evanescent modes is a reasonable assumption for long waves, but that for short waves the velocity through the porous wall from the evanescent modes can be up to 25% of the velocity from the progressive modes at the free surface. However, the effect of neglecting the evanescent modes has only a small effect on the depth-averaged velocity through porous wall and the analytical models derived using depth-averaged assumptions are shown to give good agreement with the BEM model for the reflection coefficient, horizontal force and overturning moment on the porous barrier. The analytical models are used to investigate the effects of the drag and inertia coefficients of the porous barrier on the behaviour of the solution. It is shown that for fixed values of the drag coefficient, wave frequency and amplitude, the solutions for the reflection coefficient lie on approximately semicircular arcs on the complex plane, with the position on the arc determined by the inertial coefficient. This places bounds on the size of the phase change in the reflected and transmitted wave which are possible. The analytical models are also used to derive the asymptotic behaviour of the solution in long and short waves. The implications of the results for more general cases of wave interaction with porous structures are discussed.