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The evolution of a viscous gravity current in a confined geometry

Accepted version
Peer-reviewed

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Authors

Gusinow, RJ 

Abstract

jats:pWe describe a theoretical and experimental study of an axisymmetric viscous gravity current with a constant flux, confined to the space between two horizontal parallel plates. The effect of confinement results in two regions of flow: an inner region where the fluid is in contact with both plates and an outer annular region where the fluid forms a gravity current along the lower plate. We present a simple theoretical model that describes the flow dynamics by a single dimensionless parameter jats:inline-formula jats:alternatives <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112023000812_inline1.png" /> jats:tex-mathJ</jats:tex-math> </jats:alternatives> </jats:inline-formula>, which is the ratio of the characteristic height of an unconfined gravity current to the height of the confined space. Theoretical height profiles display the same characteristics as unconfined gravity currents until jats:inline-formula jats:alternatives <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112023000812_inline2.png" /> jats:tex-mathJ≈0.48</jats:tex-math> </jats:alternatives> </jats:inline-formula>, where a rapid change in behaviour occurs as confinement comes into effect. For larger values of jats:inline-formula jats:alternatives <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112023000812_inline3.png" /> jats:tex-mathJ</jats:tex-math> </jats:alternatives> </jats:inline-formula>, the confined viscous gravity current gradually tends to Hele-Shaw flow, with the transition essentially complete by jats:inline-formula jats:alternatives <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112023000812_inline4.png" /> jats:tex-mathJ≈2</jats:tex-math> </jats:alternatives> </jats:inline-formula>. We compare the findings from our theoretical model with the results of a series of experiments using golden syrup with various fluxes and gap spacings. Although the data aligns with the major aspects of the model, it is clear that other physics is at play and a single non-dimensional parameter is not sufficient to capture the flow behaviour fully. We speculate on the factors absent in our model that may be responsible for this mismatch.</jats:p>

Description

Keywords

lubrication theory

Journal Title

Journal of Fluid Mechanics

Conference Name

Journal ISSN

0022-1120
1469-7645

Volume Title

Publisher

Cambridge University Press (CUP)