Development of a Non-linear Porous Media Flow Relationship for Oscillatory Unsteady Flow

Abstract

In recent years, numerical modeling of non-stationary porous media flow resulting from wave interaction with granular media in coastal areas (such as wave interaction with breakwaters, flow in the seabed and flow in submerged granular structures) has been the topic of much research. Many models have been based on non-linear porous media flow laws such as the Forchheimer equation which is based on unidirectional, non-linear flow. This paper presents the results of testing undertaken in an oscillatory water tunnel in which various media were subjected to rapidly varying oscillatory flow, such as that experienced by granular structures subjected to wave action. Results of the experiments are compared with the Forchheimer equation. It was found that the addition of an inertial term would greatly increase the accuracy of the Forchheimer equation. However, problems still exist in predicting the steady and unsteady flow coefficients for most granular media unless carefully controlled permeameter tests are undertaken. As an alternative, the resistance of the media was formulated directly in terms of the hydraulic properties of the oscillatory flow and the properties of the medium. This new relationship resulted in excellent agreement between experimental and predicted hydraulic gradient.