Skip to main content Accessibility help
×
Home
Hostname: page-component-cf9d5c678-p4zth Total loading time: 0.241 Render date: 2021-08-01T15:12:26.725Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

Stratified gravity currents in porous media

Published online by Cambridge University Press:  22 February 2016

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
Corresponding
E-mail address:

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.

Type
Papers
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, 6778.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, 321344.CrossRefGoogle 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, 248270.CrossRefGoogle 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, 363383.CrossRefGoogle Scholar
Huppert, H. E. & Woods, A. W. 1995 Gravity-driven flows in porous layers. J. Fluid Mech. 292, 5569.CrossRefGoogle 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.CrossRefGoogle Scholar
Orr, F. M. 2009 Onshore geological storage of CO2 . Science 325, 16561658.CrossRefGoogle Scholar
Pegler, S. S., Huppert, H. E. & Neufeld, J. A. 2013a Topographic controls on gravity currents in porous media. J. Fluid Mech. 734, 317337.CrossRefGoogle Scholar
Pegler, S. S., Huppert, H. E. & Neufeld, J. A. 2014 Fluid injection into a confined porous layer. J. Fluid Mech. 745, 592620.CrossRefGoogle 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.CrossRefGoogle Scholar
Szulczewski, M. L., Hesse, M. A. & Juanes, R. 2013 Carbon dioxide dissolution in structural and stratigraphic traps. J. Fluid Mech. 736, 287315.CrossRefGoogle Scholar
Szulczewski, M. L. & Juanes, R. 2013 The evolution of miscible gravity currents in horizontal porous layers. J. Fluid Mech. 719, 8296.CrossRefGoogle Scholar
Woods, A. W. & Mason, R. 2000 The dynamics of two-layer gravity-driven flows in permeable rock. J. Fluid Mech. 421, 83114.CrossRefGoogle 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 16 MB
5
Cited by

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Stratified gravity currents in porous media
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Stratified gravity currents in porous media
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Stratified gravity currents in porous media
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *