Simulation of surface waves with porous boundaries in a 2-D numerical wave tank

Abstract

The classical water wave theories for use in coastal and offshore design have had the theoretical drawback of assuming a rigid, nonporous bottom overlain by an inviscid fluid. In most offshore areas not far from the shore, the bottom material interacts with the wave filed, usually resulting in an attenuation of the wave height due to bottom friction, percolation losses and viscous damping within the sediments. In this study, we first developed a 2-D numerical wave tank by using 2-D boundary element method (desingularized method), assuming rigid bottom. The results are verified through comparison with published results in the open literature. The reflection and transmission coefficients as well as hydrodynamic coefficients and wave forces are obtained for an arbitrary 2-D body. The boundary element method is then extended to the problem with porous boundaries. The flow inside porous medium is based on Darcy's rule. Analytic solutions are obtained for the flat porous bottom case and compared with the BEM solutions. Good agreement is observed between the two independent solutions. After verifying the numerical methods, we studied the interaction of water waves with a porous or rigid bottom-mounted half cylinder. The reflection and transmission coefficients and pore-pressure forces are calculated for various wave frequencies and permeability parameters. The limitation of using Darcy's rule is discussed.