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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.

## Abstract

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