Second-Order Shallow-Flow Theory and Dupuit Approximation for Phreatic Aquifers

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.