A Class of Exact Solutions of the Boussinesq Equation for Horizontal and Sloping Aquifers


Journal Article

© 2018. American Geophysical Union. All Rights Reserved. The nonlinear equation of Boussinesq (1877) is a foundational approach for studying groundwater flow through an unconfined aquifer, but solving the full nonlinear version of the Boussinesq equation remains a challenge. Here, we present an exact solution to the full nonlinear Boussinesq equation that not only applies to sloping aquifers but also accounts for source and sink terms such as bedrock seepage, an often significant flux in headwater catchments. This new solution captures the hysteretic relationship (a loop rating curve) between the groundwater flow rate and the water table height, which may be used to provide a more realistic representation of streamflow and groundwater dynamics in hillslopes. In addition, the solution provides an expression where the flow recession varies based on hillslope parameters such as bedrock slope, bedrock seepage, aquifer recharge, plant transpiration, and other factors that vary across landscape types.

Full Text

Duke Authors

Cited Authors

  • Bartlett, MS; Porporato, A

Published Date

  • February 1, 2018

Published In

Volume / Issue

  • 54 / 2

Start / End Page

  • 767 - 778

Electronic International Standard Serial Number (EISSN)

  • 1944-7973

International Standard Serial Number (ISSN)

  • 0043-1397

Digital Object Identifier (DOI)

  • 10.1002/2017WR022056

Citation Source

  • Scopus