An exact solution of solute transport by one-dimensional random velocity fields

V. D. Cvetkovic*, G. Dagan, A. M. Shapiro

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

Abstract

The problem of one-dimensional transport of passive solute by a random steady velocity field is investigated. This problem is representative of solute movement in porous media, for example, in vertical flow through a horizontally stratified formation of variable porosity with a constant flux at the soil surface. Relating moments of particle travel time and displacement, exact expressions for the advection and dispersion coefficients in the Focker-Planck equation are compared with the perturbation results for large distances. The first- and second-order approximations for the dispersion coefficient are robust for a lognormal velocity field. The mean Lagrangian velocity is the harmonic mean of the Eulerian velocity for large distances. This is an artifact of one-dimensional flow where the continuity equation provides for a divergence free fluid flux, rather than a divergence free fluid velocity.

Original languageEnglish
Pages (from-to)45-54
Number of pages10
JournalStochastic Hydrology and Hydraulics
Volume5
Issue number1
DOIs
StatePublished - Mar 1991

Keywords

  • Lagrangian description
  • Solute transport
  • nonlinear effects
  • random velocity
  • travel time

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