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Analytical solution to a sharp interface problem in a vortex‐generated flow
Author(s) -
Kacimov A. R.
Publication year - 2001
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2001wr000384
Subject(s) - wedge (geometry) , dimensionless quantity , conformal map , aquifer , geology , mechanics , vortex , boundary value problem , hydraulic head , geometry , head (geology) , mathematics , geotechnical engineering , mathematical analysis , physics , groundwater , geomorphology
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.