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Does Asymptotic Transverse Macrodispersion Exist In Steady Darcy Flow?

Abstract : A long-standing question in groundwater hydrology is whether or not transverse macrodispersion (i.e. dispersion in the absence of molecular diffusion and pore-scale dispersion) in the long-time limit exists in steady Darcy flow. After much debate, it was firmly established over 15 years ago that such dispersion is zero in steady, stationary two-dimensional (2D) Darcy flows due to the restriction that streamlines of steady incompressible flows cannot cross in 2D domains. This constraint means that the transverse distance between two streamlines may only fluctuate with longitudinal distance, leading to zero transverse macrodispersion in the asymptotic limit. In contrast, it has long been thought that such constraints do not apply to three-dimensional (3D) Darcy flow, as streamlines can now freely wander throughout the 3D aquifer domain. We revisit this question for several classes of 3D Darcy flow, and show that for locally isotropic conductivity fields, Darcy flow possesses a pair of streamfunctions. These streamfunctions organise the streamlines of the flow, confining them to 2D streamsurfaces. This confinement fundamentally alters our understanding of the kinematics of these flows and constrains the allowable set of fluid deformations within a stochastic model. We discuss these constraints and the associated implications for understanding and modelling transport, mixing and dispersion in steady 3D Darcy flow.
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Conference papers
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https://hal-insu.archives-ouvertes.fr/insu-02413332
Contributor : Isabelle Dubigeon <>
Submitted on : Monday, December 16, 2019 - 10:48:50 AM
Last modification on : Wednesday, December 18, 2019 - 1:20:27 AM

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  • HAL Id : insu-02413332, version 1

Citation

Daniel Lester, Marco Dentz, Aditya Bandopadhyay, Tanguy Le Borgne. Does Asymptotic Transverse Macrodispersion Exist In Steady Darcy Flow?. American Geophysical Union Fall Meeting 2019, American Geophysical Union, Dec 2019, San Francisco, United States. pp.H53D-08. ⟨insu-02413332⟩

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