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

14 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

Keywords

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

ASJC Scopus subject areas

  • Engineering (miscellaneous)
  • Applied Mathematics

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