Testing the limits of the spatial Markov model for upscaling transport: The role of nonmonotonic effective velocity autocorrelations

Nicole L. Sund, Diogo Bolster, and David A. Benson
Phys. Rev. E 94, 043107 – Published 13 October 2016

Abstract

The spatial Markov model is a Lagrangian random walk model, widely and successfully used for upscaling transport in heterogeneous flows across a broad range of problems. It is particularly useful at early or pre-asymptotic times when many other conventional upscaling approaches may not be valid. However, as with all upscaled models, it must have its limits. In particular, the question of what the smallest scale at which it can be legitimately applied, without violating implicit assumptions, remains. Here we address this issue by considering one of the most classical transport upscaling problems: Taylor dispersion in a bounded shear flow. We demonstrate that the smallest scale for the spatial Markov model depends on the transverse width of the domain, the variability of the flow field as quantified by a coefficient of variation, and the competition of longitudinal and transverse diffusion coefficients. We show that this scale is a factor of the Peclet number smaller than the classical Taylor dispersion scale, meaning that for advection-dominated systems where Peclet numbers are large, this model can be applied at much smaller scales than classical Taylor-Aris dispersion theories.

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  • Received 27 April 2016

DOI:https://doi.org/10.1103/PhysRevE.94.043107

©2016 American Physical Society

Physics Subject Headings (PhySH)

  1. Physical Systems
Fluid Dynamics

Authors & Affiliations

Nicole L. Sund1,2,*, Diogo Bolster2, and David A. Benson3

  • 1Division of Hydrologic Sciences, Desert Research Institute, Reno, Nevada 89512, USA
  • 2Department of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, Indiana 46545, USA
  • 3Department of Geology and Geological Engineering, Colorado School of Mines, Golden, Colorado 80401, USA

  • *nsund@dri.edu

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Issue

Vol. 94, Iss. 4 — October 2016

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