Stochastic Hydrology and Hydraulics

, Volume 11, Issue 5, pp 397–422 | Cite as

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

  • Vivek Kapoor
  • Peter K. Kitanidis


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.

Key words

Random flow field diffusion concentration fluctuations covariance variance 


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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Vivek Kapoor
    • 1
  • Peter K. Kitanidis
    • 2
  1. 1.School of Civil & Environmental EngineeringGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Department of Civil EngineeringStanford UniversityStanfordUSA

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