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Axisymmetric viscous gravity currents flowing over a porous medium

Published online by Cambridge University Press:  10 March 2009

MELISSA J. SPANNUTH ,
JEROME A. NEUFELD ,
J. S. WETTLAUFER  and
M. GRAE WORSTER
MELISSA J. SPANNUTH*
Affiliation:
Department of Geology and Geophysics, Yale University, New Haven, CT 06520, USA
JEROME A. NEUFELD
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
J. S. WETTLAUFER
Affiliation:
Department of Geology and Geophysics, Yale University, New Haven, CT 06520, USA Department of Physics, Yale University, New Haven, CT 06520, USA Nordic Institute for Theoretical Physics, Roslagstullsbacken 23, University Center, 106 91 Stockholm, Sweden
M. GRAE WORSTER
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
*
†Email address for correspondence: [email protected]
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Abstract

We study the axisymmetric propagation of a viscous gravity current over a deep porous medium into which it also drains. A model for the propagation and drainage of the current is developed and solved numerically in the case of constant input from a point source. In this case, a steady state is possible in which drainage balances the input, and we present analytical expressions for the resulting steady profile and radial extent. We demonstrate good agreement between our experiments, which use a bed of vertically aligned tubes as the porous medium, and the theoretically predicted evolution and steady state. However, analogous experiments using glass beads as the porous medium exhibit a variety of unexpected behaviours, including overshoot of the steady-state radius and subsequent retreat, thus highlighting the importance of the porous medium geometry and permeability structure in these systems.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 622 , 10 March 2009 , pp. 135 - 144
Copyright
Copyright © Cambridge University Press 2009

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References

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