HR: 14:05h
AN: H22G-02    [PDF]
TI: Improving the Dupuit-Forchheimer Approximation for Free Surface Flow in an Unconfined Aquifer
AU: * Knight, J H
EM: John.Knight@csiro.au
AF: CSIRO Land and Water, GPO Box 1666, Canberra, ACT 2601 Australia
AB: The classical Dupuit-Forchheimer (DF) approximation for groundwater free surface flow in an unconfined aquifer assumes that the vertical component of the seepage velocity is zero. This assumption is expected to be least accurate when there is non-zero accretion at the free surface. The DF approximation leads to a nonlinear diffusion equation satisfied by the height of the free surface. The general principles of integral methods used by Yves Parlange are to assume some simple approximate shape for some unknown function, and then to choose the parameters of this function to satisfy some known integral relation of the flow system. The DF approximation is improved by assuming that the vertical velocity component is zero at the impermeable horizontal base, and increases linearly to its unknown value at the free surface. The well known Guirinsky potential which depends only on the free surface height corresponds to the DF assumptions. Youngs used an integral relation to define a new potential which depends on the free surface height and also on the vertical velocity component, and which for steady flow satisfies a Poisson equation in the horizontal coordinates. We use the assumption of linear variation of vertical velocity to calculate an approximation to the Youngs potential. In some simple flow systems such as the classical dam problem this leads to a simple differential equation for the free surface height, which can be solved numerically. ln some cases simple explicit approximations can be found for quantities of interest, such as the maximum free surface height between drainage ditches.
DE: 1829 Groundwater hydrology
SC: Hydrology [H]
MN: 2003 Fall Meeting