Gaussian Closure of Transient Unsaturated Flow in Random Soils

Orna Amir, Shlomo P. Neuman

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


The Gaussian closure approximation, previously used by the authors to solve steady state stochastic unsaturated flow problems in randomly heterogeneous soils, is extended here to transient flow. The method avoids linearizing the governing flow equations or the soil constitutive relations. It places no theoretical limit on the variance of constitutive parameters and applies to a broad class of soils with flow properties that scale according to a linearly separable model. Closure is obtained by treating the dimensionless pressure head ψ as a multivariate Gaussian function. It yields a system of coupled nonlinear differential equations for the first and second moments of ψ. We apply the Gaussian closure technique to the problem of transient infiltration into a randomly stratified soil. In each layer, hydraulic conductivity and water content vary exponentially with ψ. Elsewhere we show that application of the technique to other constitutive relations is straightforward. Our solution for the mean and variance of ψ in a one-dimensional layer with random conductivity compares well with Monte Carlo results over a wide range of parameters, provided that the spatial variability of the constitutive exponent is small. The solution provides considerable insight into the behavior of the transient unsaturated stochastic flow problem.

Original languageEnglish (US)
Pages (from-to)55-77
Number of pages23
JournalTransport in Porous Media
Issue number1
StatePublished - Jan 2004


  • Gaussian closure
  • Porous media
  • Random heterogeneity
  • Stochastic equations
  • Transient flow
  • Unsaturated flow

ASJC Scopus subject areas

  • Catalysis
  • General Chemical Engineering


Dive into the research topics of 'Gaussian Closure of Transient Unsaturated Flow in Random Soils'. Together they form a unique fingerprint.

Cite this