Transport in multiscale log conductivity fields with truncated power variograms

Vittorio Di Federico, Shlomo P Neuman

Research output: Contribution to journalArticle

54 Citations (Scopus)

Abstract

Di Federico and Neuman [this issue] investigated mean uniform steady state groundwater flow in an unbounded domain with log hydraulic conductivity that forms a truncated multiscale hierarchy of statistically homogeneous and isotropic Gaussian fields, each associated with an exponential autocovariance. Here we present leading-order expressions for the displacement covariance, and dispersion coefficient, of an ensemble of solute particles advected through such a flow field in two or three dimensions. Both quantities are functions of the mean travel distance s, the Hurst coefficient H, and the low- and high-frequency cutoff integral scales λ(l) and λ(u). The latter two are related to the length scales of the sampling window (region under investigation) and sample volume (data support), respectively. If one considers transport to be affected by a finite domain much larger than the mean travel distance, so that s << λ(l) < ∞, then an early preasymptotic regime develops during which longitudinal and transverse dispersivities grow linearly with s. If one considers transport to be affected by a domain which increases in proportion to s, then λ(l) and s are of similar order and a preasymptotic regime never develops. Instead, transport occurs under a regime that is perpetually close to asymptotic under the control of an evolving scale λ(l) ~ s. We show that if, additionally, λ(u) << λ(l), then the corresponding longitudinal dispersivity grows in proportion to λ(l)/(1+2H) or, equivalently, s(1+2H). Both these preasymptotic and asymptotic theoretical growth rates are shown to be consistent with the observed variation of apparent longitudinal Fickian dispersivities with scale. We conclude by investigating the effect of variable separations between cutoff scales on dispersion.

Original languageEnglish (US)
Pages (from-to)963-973
Number of pages11
JournalWater Resources Research
Volume34
Issue number5
StatePublished - May 1998

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dispersivity
variogram
travel
conductivity
Groundwater flow
Hydraulic conductivity
groundwater flow
Cutoff frequency
hydraulic conductivity
solutes
Flow fields
Sampling
sampling
flow field
solute

ASJC Scopus subject areas

  • Aquatic Science
  • Environmental Science(all)
  • Environmental Chemistry
  • Water Science and Technology

Cite this

Transport in multiscale log conductivity fields with truncated power variograms. / Di Federico, Vittorio; Neuman, Shlomo P.

In: Water Resources Research, Vol. 34, No. 5, 05.1998, p. 963-973.

Research output: Contribution to journalArticle

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