Journal of Fluid Mechanics



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Intrusive gravity currents in two-layer fluids


BRUCE R. SUTHERLAND a1, PATRICK J. KYBA a1 and MORRIS R. FLYNN a1
a1 Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, Canada, T6G 2G1

Article author query
sutherland br   [Google Scholar] 
kyba pj   [Google Scholar] 
flynn mr   [Google Scholar] 
 

Abstract

We investigate the dynamics of a gravity current that propagates along the interface of a two-layer fluid. The results of the well-studied symmetric case are reproduced in which the upper- and lower-layer depth of the ambient are equal and the density of the intrusion is the average density of the ambient. In addition, we present the first detailed examination of asymmetric circumstances in which the density of the intrusion differs from the mean density of the ambient and in which the upper- and lower-layer fluid depths are unequal. The general equations derived by J. Y. Holyer & H. E. Huppert (J. Fluid Mech.) vol. 100, 1980, pp. 739–767,), which predict the speed and vertical extent of the gravity current head, are re-expressed in a simpler form that employs the Boussinesq approximation. Approximate analytic solutions are determined using perturbation theory. The predictions are compared with the results of laboratory experiments. We find excellent agreement if the density of the gravity current is the average of the upper- and lower-layer densities weighted by the respective depths of the two layers. However, exact theory significantly underpredicts the gravity current speeds if the current density differs from this weighted-mean average. The discrepancy is attributed to the generation of waves that lead and trail the gravity current head. Empirical support for this assertion is provided through an examination of the observed wave characteristics.

(Received May 1 2003)
(Revised May 10 2004)



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