NONLINEAR DIFFUSIVE SURFACE-WAVES IN POROUS-MEDIA

A fully nonlinear, diffusive, and weakly dispersive wave equation is d erived for describing gravity surface wave propagation in a shallow po rous medium. Darcy's flow is assumed in a homogeneous and isotropic po rous medium. In deriving the general equation, the depth of the porous medium is assumed to be small in comparison with the horizontal lengt h scale, i.e. O(mu(2)) = O(h(0)/L)(2) much less than 1. The order of m agnitude of accuracy of the general equation is O(mu(4)). Simplified g overning equations are also obtained for the situation where the magni tude of the free-surface fluctuations is also small, O(epsilon) = O(a/ h(0)) much less than 1, and is of the same order of magnitude as O(mu( 2)). The resulting equation is of O(mu(4),epsilon(2)) and is equivalen t to the Boussinesq equations for water waves. Because of the dissipat ive nature of the porous medium flow, the damping rate of the surface wave is of the same order magnitude as the wavenumber. The tide-induce d groundwater fluctuations are investigated by using the newly derived equation. Perturbation solutions as well as numerical solutions are o btained. These solutions compare very well with experimental data. The interactions between a solitary wave and a. rectangular porous breakw ater are then examined by solving the Boussinesq equations and the new ly derived equations together. Numerical solutions for transmitted wav es for different porous breakwaters are obtained and compared with exp erimental data. Excellent agreement is observed.