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A note on the propagation speed of a weakly dissipative gravity current

Published online by Cambridge University Press:  15 February 2007

EUGENY V. ERMANYUK  and
NIKOLAI V. GAVRILOV
EUGENY V. ERMANYUK
Affiliation:
Lavrentyev Institute of Hydrodynamics, 630090, Novosibirsk, Russiaermanyuk@hydro.nsc.ru
NIKOLAI V. GAVRILOV
Affiliation:
Lavrentyev Institute of Hydrodynamics, 630090, Novosibirsk, Russiaermanyuk@hydro.nsc.ru
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Abstract

This paper presents an experimental study on the propagation speed of gravity currents at moderate values of a gravity Reynolds number. Two cases are considered: gravity currents propagating along a rigid boundary and intrusive gravity currents. For the first case, a semi-empirical formula for the front propagation speed derived from simple energy arguments is shown to capture well the effect of flow deceleration because of viscous dissipation. In the second case, the propagation speed is shown to agree with the one predicted for energy-conserving virtually inviscid flows (Shin, Dalziel & Linden, J. Fluid Mech. vol. 521, 2004, p. 1), which implies that the losses due to vorticity generation and mixing at the liquid–liquid interface play only a minor role in the total balance of energy.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 574 , 10 March 2007 , pp. 393 - 403
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Benjamin, T. B. 1968 Gravity currents and related phenomena. J. Fluid Mech. 31, 209–248.Google Scholar
Birman, V. K., Martin, J. E. & Meiburg, E. 2005 The non-Boussinesq lock-exchange problem. Part 2. High-resolution simulations. J. Fluid Mech. 537, 125–144.CrossRefGoogle Scholar
Britter, R. E. & Simpson, J. E. 1981 A note on the structure of the head of an intrusive gravity current. J. Fluid Mech. 112, 459–466.Google Scholar
Cheong, H.-B., Kuenen, J. J. P. & Linden, P. F. 2006 The front speed of intrusive gravity currents. J. Fluid Mech. 552, 1–11.Google Scholar
Hoult, D. P. 1972 Oil spreading on the sea. Annu. Rev. Fluid Mech. 4, 341–368.Google Scholar
Huppert, H. E. 1982 The propagation of two-dimensional and axisymmetric viscous gravity currents over a rigid horizontal surface. J. Fluid Mech. 121, 43–58.Google Scholar
Huppert, H. E. & Simpson, J. E. 1980 The slumping of gravity currents. J. Fluid Mech. 99, 785–799.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1987 Fluid Mechanics. Butterworth-Heineman.Google Scholar
Lowe, R. J., Linden, P. F. & Rottman, J. W. 2002 A laboratory study of the velocity structure in an intrusive gravity current. J. Fluid Mech. 456, 33–48.CrossRefGoogle Scholar
Lowe, R. J., Rottman, J. W. & Linden, P. F. 2005 The non-Boussinesq lock-exchange problem. Part 1. Theory and experiments. J. Fluid Mech. 537, 101–124.CrossRefGoogle Scholar
Marino, B. M., Thomas, L. P. & Linden, P. F. 2005 The front condition for gravity currents. J. Fluid Mech. 536, 49–78.CrossRefGoogle Scholar
Rooij, F., Linden, P. F. & Dalziel, S. B. 1999 Saline- and particle-driven interfacial intrusions. J. Fluid Mech. 389, 303–334.Google Scholar
Rottman, J. W. & Simpson, J. E. 1983 Gravity currents produced by instantaneous releases of a heavy fluid in a rectangular channel. J. Fluid Mech. 135, 95–110.Google Scholar
Shin, J. O., Dalziel, S. B. & Linden, P. F. 2004 Gravity currents produced by lock exchange. J. Fluid Mech. 521, 1–34.Google Scholar
Simpson, J. S. 1997 Gravity Currents: In the Environment and the Laboratory, 2nd edn. Cambridge University Press.Google Scholar
Sutherland, B. R., Kyba, P. J. & Flynn, M. R. 2004 Intrusive gravity currents in two-layer fluids. J. Fluid Mech. 514, 327–353.Google Scholar