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Viscous lock-exchange in rectangular channels

Published online by Cambridge University Press:  14 February 2011

J. MARTIN ,
N. RAKOTOMALALA ,
L. TALON  and
D. SALIN
J. MARTIN
Affiliation:
Université Pierre et Marie Curie, Université Paris-Sud, CNRS, Laboratoire FAST, Bâtiment 502, Rue du Belvedere, Campus Universitaire, F-91405 Orsay CEDEX, France
N. RAKOTOMALALA
Affiliation:
Université Pierre et Marie Curie, Université Paris-Sud, CNRS, Laboratoire FAST, Bâtiment 502, Rue du Belvedere, Campus Universitaire, F-91405 Orsay CEDEX, France
L. TALON
Affiliation:
Université Pierre et Marie Curie, Université Paris-Sud, CNRS, Laboratoire FAST, Bâtiment 502, Rue du Belvedere, Campus Universitaire, F-91405 Orsay CEDEX, France
D. SALIN*
Affiliation:
Université Pierre et Marie Curie, Université Paris-Sud, CNRS, Laboratoire FAST, Bâtiment 502, Rue du Belvedere, Campus Universitaire, F-91405 Orsay CEDEX, France
*
†Email address for correspondence: [email protected]
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Abstract

In a viscous lock-exchange gravity current, which describes the reciprocal exchange of two fluids of different densities in a horizontal channel, the front between two Newtonian fluids spreads as the square root of time. The resulting diffusion coefficient reflects the competition between the buoyancy-driving effect and the viscous damping, and depends on the geometry of the channel. This lock-exchange diffusion coefficient has already been computed for a porous medium, a two-dimensional (2D) Stokes flow between two parallel horizontal boundaries separated by a vertical height H and, recently, for a cylindrical tube. In the present paper, we calculate it, analytically, for a rectangular channel (horizontal thickness b and vertical height H) of any aspect ratio (H/b) and compare our results with experiments in horizontal rectangular channels for a wide range of aspect ratios (1/10 to 10). We also discuss the 2D Stokes–Darcy model for flows in Hele-Shaw cells and show that it leads to a rather good approximation, when an appropriate Brinkman correction is used.

JFM classification

Geophysical and Geological Flows: Gravity currents
Type
Papers
Information
Journal of Fluid Mechanics , Volume 673 , 25 April 2011 , pp. 132 - 146
Copyright
Copyright © Cambridge University Press 2011

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