Fluid dynamics of nonaqueous phase contaminants in groundwater: Analytical solutions and analogy with zhukovsky’s trochoid

V. Obnosov Yu, Anvar Kassimov

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

An exact solution to a free-boundary, potential, 2-D flow of a Darcian fluid (mathematically equivalent to flow of a heavy irrotational ideal fluid) past a barrier is obtained by the theory of holomorphic functions. A volume of liquid contaminant contrasting in density with the ambient flowing groundwater makes a lens attached to the stoss or lee side of the barrier. The shape of the interface morphs in response to a pressure-velocity field in the dynamic and static liquid phases. The flow net and interface are plotted from explicit expressions found for the complex potential and complex velocity. As a particular case, we obtain a famous Zhukovsky’s gas-bubble contour belonging to the class of trochoids. Serious caveats for remediation projects and artificial recharge of groundwater are inferred: more intensive descending seepage of ponded surface water through a heterogeneous aquifer may worsen the groundwater quality, contrary to what would occur in homogeneous porous media.

Original languageEnglish
Title of host publicationProceedings of the World Congress on Engineering 2012, WCE 2012
EditorsLen Gelman, Andrew Hunter, A. M. Korsunsky, S. I. Ao, David WL Hukins
PublisherNewswood Limited
Pages44-47
Number of pages4
Volume2197
ISBN (Print)9789881925138
Publication statusPublished - Jan 1 2012
Event2012 World Congress on Engineering, WCE 2012 - London, United Kingdom
Duration: Jul 4 2012Jul 6 2012

Other

Other2012 World Congress on Engineering, WCE 2012
CountryUnited Kingdom
CityLondon
Period7/4/127/6/12

Keywords

  • Clean-up
  • Conformal mappings
  • Darcian flow
  • Environmental engineering
  • Free surface
  • Groundwater contamination
  • Hodograph transform
  • Holomorphic functions

ASJC Scopus subject areas

  • Computer Science (miscellaneous)

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  • Cite this

    Obnosov Yu, V., & Kassimov, A. (2012). Fluid dynamics of nonaqueous phase contaminants in groundwater: Analytical solutions and analogy with zhukovsky’s trochoid. In L. Gelman, A. Hunter, A. M. Korsunsky, S. I. Ao, & D. WL. Hukins (Eds.), Proceedings of the World Congress on Engineering 2012, WCE 2012 (Vol. 2197, pp. 44-47). Newswood Limited.