Second-Order Shallow-Flow Theory and Dupuit Approximation for Phreatic Aquifers
Publication: Journal of Hydraulic Engineering
Volume 140, Issue 9
Abstract
One-dimensional (1D) hydraulic models for phreatic aquifers are commonly based on Dupuit’s approximation for near-horizontal flows. In the past, improved 1D models were developed by inclusion of streamline curvature in the governing equations. However, the models developed for steady flow are quite different from those developed for unsteady curvilinear flow. In this paper, a single mathematical model is proposed for application to both steady and unsteady curvilinear phreatic flows. Unsteady flow equations for phreatic aquifers are presented by adopting the shallow flow approximation. The resulting model converges to that originating from perturbation methods, thereby providing a generalized result. Limitations of the second-order shallow flow theory and Dupuit’s approximation are investigated for steady flow through a dam and unsteady flow in the bank storage problems. The results obtained from the present model are compared with two-dimensional data, indicating that Dupuit’s theory is valid under a wider range of conditions than previously found.
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Published In
Journal of Hydraulic Engineering
Volume 140 • Issue 9 • September 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Jan 4, 2014
Accepted: Mar 31, 2014
Published online: May 15, 2014
Published in print: Sep 1, 2014
Discussion open until: Oct 15, 2014
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