ABSTRACT:

A numerical scheme has been developed to simulate the propagation of water waves over a rigid porous bed. The governing equations for the fluid in the water region are the Navier-Stokes equations. In the governing equations for the motion of a viscous fluid in the porous bed, both the inertial and viscous forces are taken into account. The boundary conditions on the free surface and at the interface of the water and the porous bed are exact. The incoming waves were generated by a piston type wavemaker set up in the computational domain. The numerical results were verified by comparison with the experimental data. The main characteristics of the flow fields in both the water region and the porous bed are discussed by specifying the velocity fields. The effects of a dimensionless parameter, which represents the ratio of the interracial force to the inertial force acting on the porous fluid, on the wave height attenuation were studied and discussed

INTRODUCTION

The propagation of water waves over the permeable sea bottom has been studied by many researchers. Putnam (1949) determined the loss of wave energy due to percolation in a permeable sea bottom. Putnam assumed that the percolation in a permeable sea bed caused by waves is governed by Darcy's law. In addition he assumed that the pressure variation at the sea bed interface is the same as that derived from the classical wave theory for undamped waves over an impermeable bottom. It can be seen when the depth of the permeable sea bed exceeds 0.3 times the wave length, any extension of the permeable layer no longer has appreciable effect upon the energy dissipation. Wave height is reduced due to the dissipation of the mechanical energy accompanying the viscous flow of water within the sandy bottom.

This content is only available via PDF.
You can access this article if you purchase or spend a download.