Phreatic surface flow from a near-reservoir saturated tongue

A. R. Kacimov*, Yu V. Obnosov, J. Perret

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)


Steady and transient 2D Darcian flows in a saturated 'tongue' adjacent to a reservoir are studied analytically. First, a stable tongue receiving water from an inclined equipotential reservoir bed and losing moisture through a phreatic surface is considered. The hydraulic head is governed by the Laplace equation and the complex potential and complex coordinate are determined explicitly by the Polubarinova-Kochina method at an arbitrary bank slopes and evapotranspiration rates. In a particular case of a vertical slope, the tongue becomes a right-angled triangle extending into the layer for the same distance as the Dupuit-Forchheimer model predicts. Second, a saturated Dupuit-Forchheimer flow in the tongue is analyzed under the assumption of evaporation exponentially and linearly decreasing with the depth of a phreatic surface. The corresponding non-linear ordinary differential equation is integrated twice and predicts the length of the tongue as a function of the reservoir water level. Third, a transient regime is modelled by the Boussinesq equation with evaporation uniform in space, but varying cyclostationary with time. A straight-line water table translating upward-downward is found to be located always below the water table for steady regimes with an average evaporation.

Original languageEnglish
Pages (from-to)271-281
Number of pages11
JournalJournal of Hydrology
Issue number1-4
Publication statusPublished - Aug 20 2004


  • Analytic functions
  • Boussinesq equation
  • Dupuit-Forchheimer model
  • Groundwater
  • Hodograph
  • Phreatic surface

ASJC Scopus subject areas

  • Water Science and Technology


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