Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-14T06:31:42.419Z Has data issue: false hasContentIssue false
  • English
  • Français

Stratified gravity currents in porous media

Published online by Cambridge University Press:  22 February 2016

Samuel S. Pegler ,
Herbert E. Huppert  and
Jerome A. Neufeld
Samuel S. Pegler*
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK Queens’ College, University of Cambridge, Cambridge, UK
Herbert E. Huppert
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK Faculty of Science, University of Bristol, Bristol, UK School of Mathematics and Statistics, University of New South Wales, Sydney, Australia
Jerome A. Neufeld
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK BP Institute, University of Cambridge, Cambridge, UK Department of Earth Sciences, University of Cambridge, Cambridge, UK
*
†Email address for correspondence: ssp23@cam.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider theoretically and experimentally the propagation in porous media of variable-density gravity currents containing a stably stratified density field, with most previous studies of gravity currents having focused on cases of uniform density. New thin-layer equations are developed to describe stably stratified fluid flows in which the density field is materially advected with the flow. Similarity solutions describing both the fixed-volume release of a distributed density stratification and the continuous input of fluid containing a distribution of densities are obtained. The results indicate that the density distribution of the stratification significantly influences the vertical structure of the gravity current. When more mass is distributed into lighter densities, it is found that the shape of the current changes from the convex shape familiar from studies of the uniform-density case to a concave shape in which lighter fluid accumulates primarily vertically above the origin of the current. For a constant-volume release, the density contours stratify horizontally, a simplification which is used to develop analytical solutions. For currents introduced continuously, the horizontal velocity varies with vertical position, a feature which does not apply to uniform-density gravity currents in porous media. Despite significant effects on vertical structure, the density distribution has almost no effect on overall horizontal propagation, for a given total mass. Good agreement with data from a laboratory study confirms the predictions of the model.

JFM classification

Geophysical and Geological Flows: Gravity currents Low-Reynolds-number flows: Porous media Geophysical and Geological Flows: Stratified flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 791 , 25 March 2016 , pp. 329 - 357
Check for updates
Copyright
© 2016 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Acheson, D. J. 1990 Elementary Fluid Dynamics. Clarendon.Google Scholar
Barenblatt, G. I. 1952 On some unsteady motions of fluids and gases in a porous medium. Prik. Mat. Mekh. 16, 67–78.Google Scholar
Bear, J. 1988 Dynamics of Fluids in Porous Media. Dover.Google Scholar
Daniels, P. G. & Punpocha, M. 2005 On the boundary-layer structure of cavity flow in a porous medium driven by differential heating. J. Fluid Mech. 532, 321–344.Google Scholar
Golding, M. J., Neufeld, J. A., Hesse, M. A. & Huppert, H. E. 2011 Two-phase gravity currents in porous media. J. Fluid Mech. 678, 248–270.Google Scholar
Hesse, M. A., Tchelepi, H. A., Cantwell, B. J. & Orr, F. M. 2007 Gravity currents in horizontal porous layers: transition from early to late self-similarity. J. Fluid Mech. 577, 363–383.Google Scholar
Huppert, H. E. & Woods, A. W. 1995 Gravity-driven flows in porous layers. J. Fluid Mech. 292, 55–69.Google Scholar
MacMinn, C. W., Neufeld, J. A., Hesse, M. A. & Huppert, H. E. 2012 Spreading and convective dissolution of carbon dioxide in vertically confined, horizontal aquifers. Water Resour. Res. 48, W11516.Google Scholar
Orr, F. M. 2009 Onshore geological storage of CO2 . Science 325, 1656–1658.CrossRefGoogle ScholarPubMed
Pegler, S. S., Huppert, H. E. & Neufeld, J. A. 2013a Topographic controls on gravity currents in porous media. J. Fluid Mech. 734, 317–337.Google Scholar
Pegler, S. S., Huppert, H. E. & Neufeld, J. A. 2014 Fluid injection into a confined porous layer. J. Fluid Mech. 745, 592–620.Google Scholar
Pegler, S. S., Kowal, K. N., Hasenclever, L. Q. & Worster, M. G. 2013b Lateral controls on grounding-line dynamics. J. Fluid Mech. 722, R1.Google Scholar
Szulczewski, M. L., Hesse, M. A. & Juanes, R. 2013 Carbon dioxide dissolution in structural and stratigraphic traps. J. Fluid Mech. 736, 287–315.Google Scholar
Szulczewski, M. L. & Juanes, R. 2013 The evolution of miscible gravity currents in horizontal porous layers. J. Fluid Mech. 719, 82–96.Google Scholar
Woods, A. W. & Mason, R. 2000 The dynamics of two-layer gravity-driven flows in permeable rock. J. Fluid Mech. 421, 83–114.Google Scholar

Pegler et al. supplementary movie

Lock release of a linearly stratified fluid layer in a Hele-Shaw cell. The clear fluid is slightly salty water. The blue fluid is dyed freshwater.

Download Pegler et al. supplementary movie(Video)
Video 15.9 MB