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Transport in Porous Media

, Volume 26, Issue 1, pp 109–119 | Cite as

Vorticity in Three-Dimensionally Random Porous Media

  • Vivek Kapoor
Article

Abstract

The flow gradient tensor controls the rate of dissipation of concentration fluctuations due to local dispersion, and therefore determines the rate of dilution of solute in a spatially random flow field. Off-diagonal terms of the flow gradient tensor quantify the rotational characteristics of the flow. A leading order description of the vorticity \((\omega = (\omega _1 ,\omega _2 ,\omega _3 ))\), of flow in a three-dimensionally random spatially correlated hydraulic conductivity field \((K({\text{x}}))\) is made by relating the vorticity spectrum to the spectrum of ln \(K({\text{x}})\). Distinct components of the vorticity are found to be linearly uncorrelated \((\overline {\omega _i \omega _j } = 0,i \ne j)\). The characteristic vorticity component in the bulk flow direction is zero \((\sigma _{\omega _1 } = 0)\), and the characteristic vorticity in the transverse directions \((\sigma _{\omega _2 } ,\sigma _{\omega _3 } )\) are inversely proportional to the hydraulic conductivity microscales in the other transverse direction, as exhibited in a numerical calculation of the vorticity.

vorticity random porous media microscales spectral method heterogeneity random field stochastic. 

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Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Vivek Kapoor
    • 1
  1. 1.School of Civil & Environmental Engineering, GeorgiaInstitute of TechnologyAtlantaU.S.A.

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