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Analytic solutions for groundwater whirls in box-shaped, 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 7 April 2004; revised 24 August 2004;
accepted 25 August 2004. Available online 26 October
2004.

## Abstract

Analytic solutions are derived for flow
through an elongated box-shaped aquifer that is bounded on the
left, right, top and bottom sides by impermeable boundaries; the
head gradient normal to the ends of the box is specified to be constant.
The aquifer consists of a number of horizontal layers, each with its own
horizontal hydraulic conductivity tensor. When all horizontal
conductivities are isotropic, streamlines are straight, but when the
horizontal anisotropy is different between layers, streamlines have the
shape of spirals. Bundles of spiraling streamlines rotating in the same
direction are called groundwater whirls. These groundwater whirls may
spread contaminants from the top of an aquifer to the bottom by advection
alone. An exact solution for an arbitrary number of layers is derived using
a multi-layer approach, which is based on the Dupuit approximation within
each layer. The multi-layer solution compares well with an exact three-
dimensional solution, which is derived by placing certain restrictions on
the variation of the hydraulic conductivity tensor. It is shown that a hypothetical
aquifer consisting of three layers may have one, two, or three groundwater whirls;
adjacent whirls rotate in opposite directions. Another notable flow pattern is
obtained with a four-layer model where one large whirl encloses two smaller ones,
all rotating in the same direction