A Dupuit formulation for flow in layered, anisotropic aquifers
Mark Bakker
, 
, a and Kick Hemker, b
a Department
of Biological and Agricultural Engineering, University of
Georgia, Athens, GA 30602, USA
b Faculty of Earth Sciences,
Vrije Universiteit, De Boelelaan 1085, 1081 HV, Amsterdam,
The Netherlands
Received 1 January 2002; revised 29 April 2002;
accepted 4 July 2002. Available online 2 November
2002.
A new theory is presented for groundwater flow in layered, anisotropic aquifers; flow must remain semi-confined. Two main approximations are made: (1) the aquifer consists of a number of horizontal, homogeneous layers, each with its own anisotropic transmissivity, and (2) the resistance to flow in the vertical direction is neglected. Analytic solutions are derived for the head and horizontal flow in each layer by use of a comprehensive transmissivity tensor. The vertical component of flow at the layer interfaces is computed analytically by vertical integration of the horizontal divergence. The theory is applied to both uniform flow and flow to a well; solutions may be superimposed. Flow in layered, anisotropic aquifers is three-dimensional when the anisotropy between layers differs. In the context of contaminant transport, the resulting three-dimensional flow field can be of great importance. Three-dimensional flow lines become especially complicated near pumping wells. In a two-layer aquifer, the flow lines to a well may be grouped into four bundles of spiraling flow lines, referred to as groundwater whirls. These whirls are bounded by two vertical planes that intersect at the well; horizontal flow along these planes is radial. For a well in a uniform flow field, the complications of the three-dimensional flow field are illustrated by the difficulties that are encountered in delineating the capture zone of the well.
Author Keywords: Layered aquifer; Anisotropy; Dupuit approximation; Capture zone