TY - JOUR

T1 - Analytical Solution for Interface Flow to a Sink With an Upconed Saline Water Lens

T2 - Strack's Regimes Revisited

AU - Kacimov, A. R.

AU - Obnosov, Y. V.

PY - 2018/1

Y1 - 2018/1

N2 - A study is made of a steady, two-dimensional groundwater flow with a horizontal well (drain), which pumps out freshwater from an aquifer sandwiched between a horizontal bedrock and ponded soil surface, and containing a lens-shaped static volume of a heavier saline water (DNAPL-dense nonaqueous phase liquid) as a free surface. For flow toward a line sink, an explicit analytical solution is obtained by a conformal mapping of the hexagon in the complex potential plane onto a reference plane and the Keldysh-Sedov integral representation of a mixed boundary-value problem for a complex physical coordinate. The interface is found as a function of the pumping rate, the well locus, the ratio of liquid densities, and the hydraulic heads at the soil surface and in the well. The shape with two inflexion points and fronts varies from a small-thickness bedrock-spread pancake to a critical curvilinear triangle, which cusps toward the sink. The problem is mathematically solvable in a relatively narrow band of geometric and hydraulic parameters. A similar analytic solution for a static heavy bubble confined by a closed-curve interface (no contact with the bedrock) is outlined as an illustration of the method to solve a mixed boundary-value problem.

AB - A study is made of a steady, two-dimensional groundwater flow with a horizontal well (drain), which pumps out freshwater from an aquifer sandwiched between a horizontal bedrock and ponded soil surface, and containing a lens-shaped static volume of a heavier saline water (DNAPL-dense nonaqueous phase liquid) as a free surface. For flow toward a line sink, an explicit analytical solution is obtained by a conformal mapping of the hexagon in the complex potential plane onto a reference plane and the Keldysh-Sedov integral representation of a mixed boundary-value problem for a complex physical coordinate. The interface is found as a function of the pumping rate, the well locus, the ratio of liquid densities, and the hydraulic heads at the soil surface and in the well. The shape with two inflexion points and fronts varies from a small-thickness bedrock-spread pancake to a critical curvilinear triangle, which cusps toward the sink. The problem is mathematically solvable in a relatively narrow band of geometric and hydraulic parameters. A similar analytic solution for a static heavy bubble confined by a closed-curve interface (no contact with the bedrock) is outlined as an illustration of the method to solve a mixed boundary-value problem.

KW - analytic functions

KW - complex potential

KW - Keldysh-Sedov formulae

KW - line/point sink

KW - Strack-type interface

KW - subcritical-critical flow

UR - http://www.scopus.com/inward/record.url?scp=85041074268&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85041074268&partnerID=8YFLogxK

U2 - 10.1002/2017WR021391

DO - 10.1002/2017WR021391

M3 - Article

AN - SCOPUS:85041074268

SN - 0043-1397

VL - 54

SP - 609

EP - 620

JO - Water Resources Research

JF - Water Resources Research

IS - 1

ER -