HR: 0830h
AN: H31D-0491    [PDF]
TI: Short- and long-time behavior of aquifer drainage after sudden drawdown according to the linearized Laplace equation.
AU: van de Giesen, N
EM: nick@uni-bonn.de
AF: Center for Development Research (ZEF), Bonn University, Walter-Flex-Str 3, Bonn, 53113 Germany
AU: * Steenhuis, T
EM: tss1@cornell.edu
AF: Department of Biological and Environmental Engineering,, Riley-Robb Hall, Cornell University, Ithaca, NY 14853 United States
AB: Ten years ago, Jean-Yves Parlange put forward a very general analytical solution for the drainage of fully penetrated aquifers ({\it van de Giesen et al.}, WRR: 94WR01733). This solution was based on the Laplace equation and linearized boundary conditions. The BC linearization assumed that the transient water table had a depth comparable to the water table as t$\to\infty$. In more recent years, {\it Parlange et al.} (WRR: 2000WR000189) put forward a re-analysis of the drainage of a horizontal aquifer after sudden drawdown, using the Boussinesq approximation. For this solution it was assumed that the water depth in the bounding drains was zero for t$>$0. Following the general approach of {\it Brutsaert and Lopez} (WRR: 97WR03068), it was determined that for this geometry the aquifer behavior could be characterized by dQ/dt$\sim$Q$^{3}$ for small t and by dQ/dt$\sim$Q$^{3/2}$ for large t. It was remarked that dQ/dt$\sim$Q for large t is often observed. In practice, it is also difficult to determine if dQ/dt$\sim$Q$^{3}$ for small t because this behavior can only be observed over a very short period. Here, we present a similar analysis of aquifer behavior based on the earlier Laplace solution for penetrated aquifers with sudden drawdown. It has been shown that also when the drain does not fully penetrate the aquifer, the solution still produces good results ({\it Szilagyi}, WRR:2002WR001564). The Laplace solution quickly shows that dQ/dt$\sim$Q for t$\to\infty$ and dQ/dt$\sim$Q$^{\infty}$ for t$\to$0. This analysis reconfirms previous findings concerning long-time behavior. More importantly, the analysis shows that the exponent B in dQ/dt$\sim$Q$^{B}$ does not have a fixed limited value for short times for the given geometry.
DE: 1829 Groundwater hydrology
DE: 1860 Runoff and streamflow
SC: Hydrology [H]
MN: 2003 Fall Meeting