Analytical solution to a sea-water intrusion problem with a fresh water zone tapering to a triple point

A. R. Kacimov, Yu V. Obnosov, M. M. Sherif, J. S. Perret

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

A new explicit analytical solution is obtained to a steady-state abrupt interface problem concerning sea-water intrusion into a coastal unconfined homogeneous aquifer with a horizontal impermeable bed and uniformly distributed losses along a phreatic surface. Two free surfaces (encroachment tongue and groundwater table) intersect with a horizontal water table of the resting sea water propagated inland. In the hodograph plane the image of the physical domain is a curvilinear triangle. Conformal mappings of the physical domain and of an unknown complex-potential domain onto an auxiliary half-plane are obtained by a modified method of Polubarinova-Kochina, which is mathematically reduced to a vector Riemann boundary-value problem. Free surfaces are reconstructed for different values of losses, densities of the two fluids, sea water and incident groundwater hydraulic heads. Comparisons with the Dupuit-Forcheimer (hydraulic) model are made and practical implications for catchment-scale groundwater management in Oman and UAE are discussed.

Original languageEnglish
Pages (from-to)197-210
Number of pages14
JournalJournal of Engineering Mathematics
Volume54
Issue number3
DOIs
Publication statusPublished - Mar 2006

Fingerprint

Tapering
Triple Point
Analytical Solution
Ground Water
Water
Groundwater
Hydraulics
Free Surface
Table
Horizontal
Riemann Boundary Value Problem
Conformal mapping
Complex Potential
Interface Problems
Hydraulic models
Interface states
Conformal Mapping
Half-plane
Aquifers
Intersect

Keywords

  • Boundary-value problems
  • Complex potential
  • Hodograph
  • Phreatic surface
  • Sharp interface

ASJC Scopus subject areas

  • Engineering (miscellaneous)
  • Applied Mathematics

Cite this

Analytical solution to a sea-water intrusion problem with a fresh water zone tapering to a triple point. / Kacimov, A. R.; Obnosov, Yu V.; Sherif, M. M.; Perret, J. S.

In: Journal of Engineering Mathematics, Vol. 54, No. 3, 03.2006, p. 197-210.

Research output: Contribution to journalArticle

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