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Advection-diffusion in spatially random flows: Formulation of concentration covariance

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Abstract

The concentration c(x,t) of a nonreactive solute undergoing advection and diffusion in a spatially random divergence-free flow field is analyzed. A leading order formulation for the spatial covariance of the concentration field,\(\overline {c'\left( {x,t} \right)c'\left( {x,t} \right)} \), is made. That formulation includes the velocity variability induced macrodispersive flux of the covariance field, and the smoothing effects of diffusion. Previous formulations of the concentration covariance had dropped at least one of these effects. It is shown that both these effects need to be included to obtain a qualitatively correct description of the concentration fluctuations.

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Authors and Affiliations

  1. School of Civil & Environmental Engineering, Georgia Institute of Technology, 30332-0355, Atlanta, GA, USA

    Vivek Kapoor

  2. Department of Civil Engineering, Stanford University, 94305-4020, Stanford, CA, USA

    Peter K. Kitanidis

Authors
  1. Vivek Kapoor
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  2. Peter K. Kitanidis
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Kapoor, V., Kitanidis, P.K. Advection-diffusion in spatially random flows: Formulation of concentration covariance. Stochastic Hydrol Hydraul 11, 397–422 (1997). https://doi.org/10.1007/BF02427926

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