WATER RESOURCES RESEARCH, VOL. 42, W12419, doi:10.1029/2006WR004901, 2006

Analytical solutions for whirling groundwater flow in two-dimensional heterogeneous anisotropic aquifers

Kick Hemker

Hydrology and Geo-Environmental Sciences, Vrije Universiteit Amsterdam, Amsterdam, Netherlands

Mark Bakker

Water Resources Section, Faculty of Civil Engineering and Geosciences, Delft University of Technology, Delft, Netherlands


Analytical solutions are derived for steady state groundwater flow in a heterogeneous, anisotropic, semiconfined aquifer. The aquifer consists of a number of horizontal layers, while each layer consists of a number of homogeneous cells with different hydraulic conductivity tensors. An exact solution for an arbitrary number of layers and cells is derived using a multilayer approach. Hypothetical models are used to study how flow is affected by heterogeneity in the anisotropy. When the major principal direction of the transmissivity tensor varies between layers, streamlines have the shape of spirals. Bundles of spiraling streamlines rotating in the same direction are called “groundwater whirls.” Analytical and numerical models of hypothetical cases produce the same flow patterns of groundwater whirls. Projected streamlines may be represented by stream function contours, which allows for easy interpretation of the main characteristics of complex whirl patterns. Typical whirl patterns may be identified in relatively simple models. Clockwise and counterclockwise whirl axes occur at the interfaces of adjacent layers. One or more clockwise whirls may occur within one counterclockwise whirl, and vice versa. The practical consequence of groundwater whirls is that the exchange of water between aquifer layers is intensified. This may have a significant impact on contaminant spreading.

Received 16 January 2006; accepted 30 August 2006; published 23 December 2006.

Keywords: analytical solution; layered aquifer; heterogeneity; anisotropy; streamlines; stream function.

Index Terms: 1828 Hydrology: Groundwater hydraulics; 1832 Hydrology: Groundwater transport; 1847 Hydrology: Modeling.

Citation: Hemker, K., and M. Bakker (2006), Analytical solutions for whirling groundwater flow in two-dimensional heterogeneous anisotropic aquifers, Water Resour. Res., 42, W12419, doi:10.1029/2006WR004901.