Abstract
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 language | English |
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Pages (from-to) | 271-281 |
Number of pages | 11 |
Journal | Journal of Hydrology |
Volume | 296 |
Issue number | 1-4 |
DOIs | |
Publication status | Published - Aug 20 2004 |
Keywords
- Analytic functions
- Boussinesq equation
- Dupuit-Forchheimer model
- Groundwater
- Hodograph
- Phreatic surface
ASJC Scopus subject areas
- Water Science and Technology