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.
UR - http://www.scopus.com/inward/record.url?scp=0035698711&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0035698711&partnerID=8YFLogxK
U2 - 10.1029/2001WR000384
DO - 10.1029/2001WR000384
M3 - Article
AN - SCOPUS:0035698711
SN - 0043-1397
VL - 37
SP - 3387
EP - 3391
JO - Water Resources Research
JF - Water Resources Research
IS - 12
ER -