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The propagation of two-dimensional and axisymmetric viscous gravity currents at a fluid interface

Published online by Cambridge University Press:  26 April 2006

John R. Lister  and
Ross C. Kerr
John R. Lister
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK Present address: Research School of Earth Sciences, The Australian National University, GPO Box 4, Canberra, ACT 2601, Australia.
Ross C. Kerr
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK Present address: Research School of Earth Sciences, The Australian National University, GPO Box 4, Canberra, ACT 2601, Australia.
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Abstract

Viscous gravity currents resulting from the introduction of fluid between an upper layer of fluid of lesser density and a lower layer of greater density are analysed. The nonlinear equations governing the spread and shape of the intrusion are formulated for the cases of intrusion at low Reynolds number between deep ambient layers and of flow over a shallow layer of viscous fluid with a rigid lower boundary. Similarity solutions of these equations are obtained in both two-dimensional and axisymmetric geometries, under the assumption that the volume of intruding fluid increases with time like tα. The theoretical predictions are shown to be in reasonable agreement with experimental observations of the spreading of glucose syrups and of viscous hydrocarbons between fluid layers of differing densities. Scaling arguments are used to derive many new results for the rates of spread of intrusions in a wide variety of further situations. A compendium of spreading relations, including some previously isolated results, is derived within a coherent framework and tabulated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 203 , June 1989 , pp. 215 - 249
Copyright
© 1989 Cambridge University Press

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