Abstract
Conformal mappings and integral representations of the Dirichlet boundary value problem for analytic functions are employed to solve explicitly the problem of steady, two-dimensional, Darcian seepage from a reservoir with fresh water to a sea in a confined aquifer of a finite thickness. A sharp interface between moving fresh and stagnant saline water forming a wedge is determined depending on one dimensionless parameter, which includes the difference in water elevations between the reservoir and the sea, the contrast in water densities, and the aquifer thickness: If the acting head reaches some critical(minimal) value, saline water will always stay at some depth; that is, the wedge will have an infinite width. In this case the interface coincides with the Saffman-Taylor shape of a finger in a Hele-Shaw apparatus.
| Original language | English |
|---|---|
| Pages (from-to) | 3387-3391 |
| Number of pages | 5 |
| Journal | Water Resources Research |
| Volume | 37 |
| Issue number | 12 |
| DOIs | |
| Publication status | Published - 2001 |
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ASJC Scopus subject areas
- Environmental Science(all)
- Environmental Chemistry
- Aquatic Science
- Water Science and Technology
Cite this
Analytical solution to a sharp interface problem in a vortex-generated flow. / Kacimov, A. R.
In: Water Resources Research, Vol. 37, No. 12, 2001, p. 3387-3391.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Analytical solution to a sharp interface problem in a vortex-generated flow
AU - Kacimov, A. R.
PY - 2001
Y1 - 2001
N2 - Conformal mappings and integral representations of the Dirichlet boundary value problem for analytic functions are employed to solve explicitly the problem of steady, two-dimensional, Darcian seepage from a reservoir with fresh water to a sea in a confined aquifer of a finite thickness. A sharp interface between moving fresh and stagnant saline water forming a wedge is determined depending on one dimensionless parameter, which includes the difference in water elevations between the reservoir and the sea, the contrast in water densities, and the aquifer thickness: If the acting head reaches some critical(minimal) value, saline water will always stay at some depth; that is, the wedge will have an infinite width. In this case the interface coincides with the Saffman-Taylor shape of a finger in a Hele-Shaw apparatus.
AB - Conformal mappings and integral representations of the Dirichlet boundary value problem for analytic functions are employed to solve explicitly the problem of steady, two-dimensional, Darcian seepage from a reservoir with fresh water to a sea in a confined aquifer of a finite thickness. A sharp interface between moving fresh and stagnant saline water forming a wedge is determined depending on one dimensionless parameter, which includes the difference in water elevations between the reservoir and the sea, the contrast in water densities, and the aquifer thickness: If the acting head reaches some critical(minimal) value, saline water will always stay at some depth; that is, the wedge will have an infinite width. In this case the interface coincides with the Saffman-Taylor shape of a finger in a Hele-Shaw apparatus.
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U2 - 10.1029/2001WR000384
DO - 10.1029/2001WR000384
M3 - Article
AN - SCOPUS:0035698711
VL - 37
SP - 3387
EP - 3391
JO - Water Resources Research
JF - Water Resources Research
SN - 0043-1397
IS - 12
ER -