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

V.D. Cvetkovic·G. Dagan·A.M. Shapiro
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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. ?? 1991 Springer-Verlag.

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V.D. Cvetkovic, G. Dagan, A.M. Shapiro. 1991. An exact solution of solute transport by one-dimensional random velocity fields. https://doi.org/10.1007/bf01544177

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