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The propagation of a gravity current into a linearly stratified fluid

Published online by Cambridge University Press:  06 March 2002

T. MAXWORTHY ,
J. LEILICH ,
J. E. SIMPSON  and
E. H. MEIBURG
T. MAXWORTHY
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089-1191, USA
J. LEILICH
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089-1191, USA Lehrstuhl für Strömungsmechanik, Friedrich-Alexander Universität, Erlangen-Nürnberg, 91058, Germany
J. E. SIMPSON
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
E. H. MEIBURG
Affiliation:
Department of Mechanical and Environmental Engineering, University of California-Santa Barbara, Santa Barbara, CA 93106, USA
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Abstract

The constant initial speed of propagation (V) of heavy gravity currents, of density ρC, released from behind a lock and along the bottom boundary of a tank containing a linearly stratified fluid has been measured experimentally and calculated numerically. The density difference, bottom to top, of the stratification is (ρb−ρ0) and its intrinsic frequency is N. For a given ratio of the depth of released fluid (h) to total depth (H) it has been found that the dimensionless internal Froude number, Fr = V/NH, is independent of the length of the lock and is a logarithmic function of a parameter R = (ρC−ρ0)/(ρb−ρ0), except at small values of h/H and R close to unity. This parameter, R, is one possible measure of the relative strength of the current (ρC−ρ0) and stratification (ρb−ρ0). The distance propagated by the current before this constant velocity regime ended (Xtr), scaled by h, has been found to be a unique function of Fr for all states tested. After this phase of the motion, for subcritical values of Fr, i.e. less than 1/π, internal wave interactions with the current resulted in an oscillation of the velocity of its leading edge. For supercritical values, velocity decay was monotonic for the geometries tested. A two-dimensional numerical model incorporating a no-slip bottom boundary condition has been found to agree with the experimental velocity magnitudes to within ±1:5%.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 453 , 25 February 2002 , pp. 371 - 394
Copyright
© 2002 Cambridge University Press

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