Some analytical solutions of the linearized Boussinesq equation with recharge for a sloping aquifer

Niko E C Verhoest, Peter A Troch

Research output: Contribution to journalArticle

80 Citations (Scopus)

Abstract

Subsurface flow from a hillslope can be described by the hydraulic groundwater theory as formulated by the Boussinesq equation. Several attempts have been made to solve this partial differential equation, and exact solutions have been found for specific situations. In the case of a sloping aquifer, Brutsaert [1994] suggested linearizing the equation to calculate the unit response of the hillslope. In this paper we first apply the work of Brutsaert by assuming a constant recharge to the groundwater table. The solution describes the groundwater table levels and the outflow in function of time. Then, an analytical expression is derived for the steady state solution by allowing time to approach infinity. This steady state water table is used as an initial condition to derive another analytical solution of the Boussinesq equation. This can then be used in a quasi steady state approach to compute outflow under changing recharge conditions.

Original languageEnglish (US)
Pages (from-to)793-800
Number of pages8
JournalWater Resources Research
Volume36
Issue number3
DOIs
StatePublished - 2000
Externally publishedYes

Fingerprint

Boussinesq equation
Aquifers
aquifers
Groundwater
recharge
aquifer
water table
hillslope
groundwater
outflow
subsurface flow
Partial differential equations
Hydraulics
hydraulics
fluid mechanics
Water

ASJC Scopus subject areas

  • Aquatic Science
  • Environmental Science(all)
  • Environmental Chemistry
  • Water Science and Technology

Cite this

Some analytical solutions of the linearized Boussinesq equation with recharge for a sloping aquifer. / Verhoest, Niko E C; Troch, Peter A.

In: Water Resources Research, Vol. 36, No. 3, 2000, p. 793-800.

Research output: Contribution to journalArticle

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