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Intrusive gravity currents from finite-length locks in a uniformly stratified fluid

Published online by Cambridge University Press:  10 September 2009

J. R. MUNROE
Affiliation:
Department of Physics, University of Alberta, Edmonton, AB, CanadaT6G 2G7
C. VOEGELI
Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, CanadaT6G 2G1
B. R. SUTHERLAND*
Affiliation:
Departments of Physics and Earth and Atmospheric Sciences, University of Alberta, Edmonton, AB, CanadaT6G 2G7
V. BIRMAN
Affiliation:
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA
E. H. MEIBURG
Affiliation:
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA
*
Email address for correspondence: bruce.sutherland@ualberta.ca

Abstract

Gravity currents intruding into a uniformly stratified ambient are examined in a series of finite-volume full-depth lock-release laboratory experiments and in numerical simulations. Previous studies have focused on gravity currents which are denser than fluid at the bottom of the ambient or on symmetric cases in which the intrusion is the average of the ambient density. Here, we vary the density of the intrusion between these two extremes. After an initial adjustment, the intrusions and the internal waves they generate travel at a constant speed. For small departures from symmetry, the intrusion speed depends weakly upon density relative to the ambient fluid density. However, the internal wave speed approximately doubles as the waves change from having a mode-2 structure when generated by symmetric intrusions to having a mode-1 structure when generated by intrusions propagating near the bottom. In the latter circumstance, the interactions between the intrusion and internal waves reflected from the lock-end of the tank are sufficiently strong and so the intrusion stops propagating before reaching the end of the tank. These observations are corroborated by the analysis of two-dimensional numerical simulations of the experimental conditions. These reveal a significant transfer of available potential energy to the ambient in asymmetric circumstances.

Type
Papers
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Aguilar, D. A. & Sutherland, B. R. 2006 Internal wave generation from rough topography. Phys. Fluids 18, Art. No. 066603.CrossRefGoogle Scholar
Amen, R. & Maxworthy, T. 1980 The gravitational collapse of a mixed region into a linearly stratified solution. J. Fluid Mech. 96, 6580.CrossRefGoogle Scholar
Benjamin, T. B. 1968 Gravity currents and related phenomena. J. Fluid Mech. 31, 209248.CrossRefGoogle Scholar
Birman, V. K., Meiburg, E. & Ungarish, M. 2007 On gravity currents in stratified ambients. Phys. Fluids 19, 086602–1–10. doi:10.1063/1.2756553.CrossRefGoogle Scholar
Bolster, D., Hang, A. & Linden, P. F. 2008 The front speed of intrusions into a continuously stratified medium. J. Fluid Mech. 594, 369377.CrossRefGoogle Scholar
Britter, R. E. & Simpson, J. E. 1978 Experiments on the dynamics of a gravity current head. J. Fluid Mech. 88, 223240.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, 459466.CrossRefGoogle Scholar
Cheong, H., Kuenen, J. J. P. & Linden, P. F. 2006 The front speed of intrusive gravity currents. J. Fluid Mech. 552, 111.CrossRefGoogle Scholar
Dalziel, S. B. 1992 Decay of rotating turbulence: Some particle tracking experiments. Appl. Sci. Res. 49, 217244.CrossRefGoogle Scholar
Dohan, K. & Sutherland, B. R. 2002 Turbulence time-scales in mixing box experiments. Exp. Fluids 33, 709719.CrossRefGoogle Scholar
Dohan, K. & Sutherland, B. R. 2003 Internal waves generated from a turbulent mixed region. Phys. Fluids 15, 488498.CrossRefGoogle Scholar
Flynn, M. R. & Linden, P. F. 2006 Intrusive gravity currents. J. Fluid Mech. 568, 1932002.CrossRefGoogle Scholar
Flynn, M. R. & Sutherland, B. R. 2004 Intrusive gravity currents and internal wave generation in stratified fluid. J. Fluid Mech. 514, 355383.CrossRefGoogle Scholar
Härtel, C., Meiburg, E. & Necker, F. 2000 Analysis and direct numerical simulation of the flow at a gravity-current head. Part 1. Flow topology and front speed for slip and no-slip boundaries. J. Fluid Mech. 418, 189212.CrossRefGoogle Scholar
Holyer, J. Y. & Huppert, H. E. 1980 Gravity currents entering a two-layer fluid. J. Fluid. Mech. 100, 739767.CrossRefGoogle Scholar
Huppert, H. E. & Simpson, J. E. 1980 The slumping of gravity currents. J. Fluid Mech. 99, 785799.CrossRefGoogle Scholar
Keulegan, G. H. 1957 An experimental study of the motion of saline water from locks into fresh water channels. Tech. Rep. 5168. Nat. Bur. Stand. Rept.Google Scholar
Klemp, J. B., Rotunno, R. & Skamarock, W. C. 1994 On the dynamics of gravity currents in a channel. J. Fluid Mech. 269, 169198.CrossRefGoogle Scholar
Lele, S. K. 1992 Compact finite-difference schemes with spectral-like resolution. J. Comput. Phys. 103, 1642.CrossRefGoogle Scholar
Long, R. R. 1953 Some aspects of the flow of stratified fluids. a theoretical investigation. Tellus 5, 4258.CrossRefGoogle Scholar
Long, R. R. 1955 Some aspects of the flow of stratified fluids. III. Continuous density gradients. Tellus 7, 341357.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, 3348.CrossRefGoogle Scholar
Manins, P. 1976 Intrusion into a stratified fluid. J. Fluid Mech. 74, 547560.CrossRefGoogle Scholar
Maxworthy, T., Leilich, J., Simpson, J. & Meiburg, E. H. 2002 The propagation of a gravity current in a linearly stratified fluid. J. Fluid Mech. 453, 371394.CrossRefGoogle Scholar
Monaghan, J. J. 2007 Gravity current interaction with interfaces. Annu. Rev. Fluid Mech. 39, 245261.CrossRefGoogle Scholar
Necker, F., Härtel, C., Kleiser, L. & Meiburg, E. 2005 Mixing and dissipation in particle-driven gravity currents. J. Fluid Mech. 545, 339372.CrossRefGoogle Scholar
Oster, G. 1965 Density gradients. Sci. Am. 213, 70.CrossRefGoogle 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, 95110.CrossRefGoogle Scholar
Schooley, A. & Hughes, B. 1972 An experimental and theoretical study of internal waves generated by the collapse of a two-dimensional mixed region in a density gradient. J. Fluid Mech. 51, 159175.CrossRefGoogle Scholar
Shin, J., Dalziel, S. & Linden, P. 2004 Gravity currents produced by lock exchange. J. Fluid Mech. 521, 134.CrossRefGoogle Scholar
Silva, I. P. D. D. & Fernando, H. J. S. 1998 Experiments on collapsing turbulent regions in stratified fluids. J. Fluid Mech. 358, 2960.CrossRefGoogle Scholar
Simpson, J. E. 1972 Effects of lower boundary on the head of a gravity current. J. Fluid Mech. 53, 759768.CrossRefGoogle Scholar
Simpson, J. E. 1982 Gravity currents in the laboratory, atmosphere, and ocean. Annu. Rev. Fluid Mech. 14, 213234.CrossRefGoogle Scholar
Simpson, J. E. 1997 Gravity Currents, 2nd edn. Cambridge University Press.Google Scholar
Simpson, J. E. & Britter, R. E. 1979 The dynamics of the head of a gravity current advancing over a horizontal surface. J. Fluid Mech. 94, 477495.CrossRefGoogle Scholar
Sutherland, B. R., Chow, A. N. F. & Pittman, T. P. 2007 The collapse of a mixed patch in stratified fluid. Phys. Fluids 19, 116602–1–6. doi:10.1063/1.2814331.CrossRefGoogle Scholar
Sutherland, B. R., Kyba, P. J. & Flynn, M. R. 2004 Interfacial gravity currents in two-layer fluids. J. Fluid Mech. 514, 327353.CrossRefGoogle Scholar
Sutherland, B. R. & Nault, J. T. 2007 Intrusive gravity currents propagating along thin and thick interfaces. J. Fluid Mech. 586, 109118. doi:10.1017/S0022112007007288.CrossRefGoogle Scholar
Ungarish, M. 2005 Intrusive gravity currents in a stratified ambient: Shallow-water theory and numerical results. J. Fluid Mech. 535, 287323.CrossRefGoogle Scholar
Ungarish, M. 2006 On gravity currents in a linearly stratified ambient: a generalization of Benjamin's steady-state propagation results. J. Fluid Mech. 548, 4968.CrossRefGoogle Scholar
Ungarish, M. & Huppert, H. E. 2002 On gravity currents propagating at the base of a stratified fluid. J. Fluid Mech. 458, 283301.CrossRefGoogle Scholar
Ungarish, M. & Huppert, H. E. 2004 On gravity currents propagating at the base of a stratified ambient: effects of geometrical constraints and rotation. J. Fluid Mech. 521, 69104.CrossRefGoogle Scholar
Ungarish, M. & Huppert, H. E. 2006 Energy balances for propagating gravity currents: homogeneous and stratified ambients. J. Fluid Mech. 565, 363380.CrossRefGoogle Scholar
Wu, J. 1969 Mixed region collapse with internal wave generation in a density stratified medium. J. Fluid Mech. 35, 531544.CrossRefGoogle Scholar