The Lagrangian kinematics of three-dimensional Darcy flow
Darcy's law is used widely to model flow in heterogeneous porous media via a spatially varying conductivity field. The isotropic Darcy equation imposes significant constraints on the allowable Lagrangian kinematics of the flow field and thus upon scalar transport. These constraints stem from the fact that the helicity density in these flows is identically zero and so the flow does not admit closed or knotted flow paths. This implies that steady Darcy flow possesses a particularly simple flow topology which involves streamlines that do not possess closed orbits, knots or linked vortex lines. This flow structure is termed ‘complex lamellar’ and consists of fully integrable (in the dynamical systems sense) streamlines which admit two analytic constants of motion and so preclude chaotic advection. In this study we show that these constants of motion correspond to a pair of streamfunctions which are single valued and topologically planar, and the intersections of the level sets of these invariants correspond to streamlines of the flow. We show that the streamfunctions and iso-potential surfaces of the flow form a semi-orthogonal coordinate system, that naturally recovers the topological constraints imposed on the Lagrangian kinematics of these flows. We use this coordinate system to investigate the impact of these constraints upon the kinematics of Darcy flow, including the deformation of fluid elements and transverse macrodispersion of solutes in the absence of local dispersion. These results shed new light on the relevance and limitations of isotropic Darcy flow as a model of transport, mixing and reaction in porous media.
Main Authors: | , , , |
---|---|
Other Authors: | |
Format: | artículo biblioteca |
Language: | English |
Published: |
Cambridge University Press
2021-05-11
|
Subjects: | Porous media, Mixing and dispersion, |
Online Access: | http://hdl.handle.net/10261/242717 http://dx.doi.org/10.13039/501100000781 |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
id |
dig-idaea-es-10261-242717 |
---|---|
record_format |
koha |
spelling |
dig-idaea-es-10261-2427172021-06-07T01:37:55Z The Lagrangian kinematics of three-dimensional Darcy flow Lester, Daniel R. Dentz, Marco Bandopadhyay, Aditya Le Borgne, Tanguy European Research Council Dentz, Marco [0000-0002-3940-282X] Porous media Mixing and dispersion Darcy's law is used widely to model flow in heterogeneous porous media via a spatially varying conductivity field. The isotropic Darcy equation imposes significant constraints on the allowable Lagrangian kinematics of the flow field and thus upon scalar transport. These constraints stem from the fact that the helicity density in these flows is identically zero and so the flow does not admit closed or knotted flow paths. This implies that steady Darcy flow possesses a particularly simple flow topology which involves streamlines that do not possess closed orbits, knots or linked vortex lines. This flow structure is termed ‘complex lamellar’ and consists of fully integrable (in the dynamical systems sense) streamlines which admit two analytic constants of motion and so preclude chaotic advection. In this study we show that these constants of motion correspond to a pair of streamfunctions which are single valued and topologically planar, and the intersections of the level sets of these invariants correspond to streamlines of the flow. We show that the streamfunctions and iso-potential surfaces of the flow form a semi-orthogonal coordinate system, that naturally recovers the topological constraints imposed on the Lagrangian kinematics of these flows. We use this coordinate system to investigate the impact of these constraints upon the kinematics of Darcy flow, including the deformation of fluid elements and transverse macrodispersion of solutes in the absence of local dispersion. These results shed new light on the relevance and limitations of isotropic Darcy flow as a model of transport, mixing and reaction in porous media. This work was supported by the European Research Council (T.L.B., grant number 648377) and the Spanish Ministry of Science and Innovation (M.D., grant number PID2019-106887GB-C31). Peer reviewed 2021-06-06T07:20:16Z 2021-06-06T07:20:16Z 2021-05-11 artículo http://purl.org/coar/resource_type/c_6501 Journal of Fluid Mechanics 918: A27 (2021) http://hdl.handle.net/10261/242717 10.1017/jfm.2021.362 http://dx.doi.org/10.13039/501100000781 en #PLACEHOLDER_PARENT_METADATA_VALUE# info:eu-repo/grantAgreement/EC/H2020/648377 Publisher's version https://doi.org/10.1017/jfm.2021.362 Sí open Cambridge University Press |
institution |
IDAEA ES |
collection |
DSpace |
country |
España |
countrycode |
ES |
component |
Bibliográfico |
access |
En linea |
databasecode |
dig-idaea-es |
tag |
biblioteca |
region |
Europa del Sur |
libraryname |
Biblioteca del IDAEA España |
language |
English |
topic |
Porous media Mixing and dispersion Porous media Mixing and dispersion |
spellingShingle |
Porous media Mixing and dispersion Porous media Mixing and dispersion Lester, Daniel R. Dentz, Marco Bandopadhyay, Aditya Le Borgne, Tanguy The Lagrangian kinematics of three-dimensional Darcy flow |
description |
Darcy's law is used widely to model flow in heterogeneous porous media via a spatially varying conductivity field. The isotropic Darcy equation imposes significant constraints on the allowable Lagrangian kinematics of the flow field and thus upon scalar transport. These constraints stem from the fact that the helicity density in these flows is identically zero and so the flow does not admit closed or knotted flow paths. This implies that steady Darcy flow possesses a particularly simple flow topology which involves streamlines that do not possess closed orbits, knots or linked vortex lines. This flow structure is termed ‘complex lamellar’ and consists of fully integrable (in the dynamical systems sense) streamlines which admit two analytic constants of motion and so preclude chaotic advection. In this study we show that these constants of motion correspond to a pair of streamfunctions which are single valued and topologically planar, and the intersections of the level sets of these invariants correspond to streamlines of the flow. We show that the streamfunctions and iso-potential surfaces of the flow form a semi-orthogonal coordinate system, that naturally recovers the topological constraints imposed on the Lagrangian kinematics of these flows. We use this coordinate system to investigate the impact of these constraints upon the kinematics of Darcy flow, including the deformation of fluid elements and transverse macrodispersion of solutes in the absence of local dispersion. These results shed new light on the relevance and limitations of isotropic Darcy flow as a model of transport, mixing and reaction in porous media. |
author2 |
European Research Council |
author_facet |
European Research Council Lester, Daniel R. Dentz, Marco Bandopadhyay, Aditya Le Borgne, Tanguy |
format |
artículo |
topic_facet |
Porous media Mixing and dispersion |
author |
Lester, Daniel R. Dentz, Marco Bandopadhyay, Aditya Le Borgne, Tanguy |
author_sort |
Lester, Daniel R. |
title |
The Lagrangian kinematics of three-dimensional Darcy flow |
title_short |
The Lagrangian kinematics of three-dimensional Darcy flow |
title_full |
The Lagrangian kinematics of three-dimensional Darcy flow |
title_fullStr |
The Lagrangian kinematics of three-dimensional Darcy flow |
title_full_unstemmed |
The Lagrangian kinematics of three-dimensional Darcy flow |
title_sort |
lagrangian kinematics of three-dimensional darcy flow |
publisher |
Cambridge University Press |
publishDate |
2021-05-11 |
url |
http://hdl.handle.net/10261/242717 http://dx.doi.org/10.13039/501100000781 |
work_keys_str_mv |
AT lesterdanielr thelagrangiankinematicsofthreedimensionaldarcyflow AT dentzmarco thelagrangiankinematicsofthreedimensionaldarcyflow AT bandopadhyayaditya thelagrangiankinematicsofthreedimensionaldarcyflow AT leborgnetanguy thelagrangiankinematicsofthreedimensionaldarcyflow AT lesterdanielr lagrangiankinematicsofthreedimensionaldarcyflow AT dentzmarco lagrangiankinematicsofthreedimensionaldarcyflow AT bandopadhyayaditya lagrangiankinematicsofthreedimensionaldarcyflow AT leborgnetanguy lagrangiankinematicsofthreedimensionaldarcyflow |
_version_ |
1777669532329967616 |