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The front speed of intrusions into a continuously stratified medium

Published online by Cambridge University Press:  14 December 2007

DIOGO BOLSTER
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA 92037, [email protected]
ALICE HANG
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA 92037, [email protected]
P. F. LINDEN
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA 92037, [email protected]

Abstract

This paper examines intrusive Boussinesq gravity currents, propagating into a continuously stratified fluid. We develop a model, based on energy arguments, to predict the front speed of such an intrusive gravity current from a lock release. We find that the depth at which the intrusion occurs, which corresponds to the level of neutral buoyancy (i.e. the depth where the intrusion density equals the stratified fluid density), affects the front speed. The maximum speeds occur when the intrusion travels along the top and bottom boundaries and the minimum speed occurs at mid-depth. Experiments and numerical simulations were conducted to compare to the theoretically predicted values, and good agreement was found.

Type
Papers
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Benjamin, T. B. 1968 Gravity currents and related phenomena. J. Fluid Mech. 31, 209248.CrossRefGoogle Scholar
Bewley, T. R. 1999 Linear control and estimation of nonlinear chaotic convection: harnessing the butterfly effec. Phys. Fluids 11, 11691186.CrossRefGoogle Scholar
Bewley, T. R., Moin, P. & Temam, R. 2001 DNS-based predictive control of turbulence: an optimal benchmark for feedback algorithms. J. Fluid Mech. 447, 179225.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. B., Kuenen, J. J. & Linden, P. F. 2006 The front speed of intrusive gravity currents. J. Fluid Mech. 552, 111.CrossRefGoogle Scholar
Dalziel, S. B. 2004 Digiflow user manual. http://www.damtp.com.ac.uk/lab/digiflow.Google Scholar
Flynn, M. R. & Linden, P. F. 2006 Intrusive gravity currents. J. Fluid Mech. 568, 193202.CrossRefGoogle Scholar
Holyer, J. Y. & Huppert, H. E. 1980 Gravity currents entering a two-layer fluid. J. Fluid. Mech. 100, 739767.CrossRefGoogle 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
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
Munroe, J. R. & Sutherland, B. R. 2006 Intrusions and internal waves in stratified fluids. Proc. Sixth Intl Symp. on Stratified Flows – Perth (ed. Ivey, G.), pp. 446–451.Google Scholar
Oster, G. 1965 Density gradients. Sci. Am. 213, 70.CrossRefGoogle Scholar
Patterson, M. D., Simpson, J. E., Dalziel, S. B. & vanHeijst, G. J. F. Heijst, G. J. F. 2006 Vortical motion in the head of an axisymmetric gravity current. Physics of Fluid 18, 8697.CrossRefGoogle Scholar
deRooij, F. Rooij, F., Linden, P. F. & Dalziel, S. B. 1999 Saline and particle-driven interfacial intrusions. J. Fluid Mech. 389, 303334.Google Scholar
Rottman, J. W. & Simpson, J. E. 1989 The formation of internal bores in the atmosphere: A laboratory model. Q. J. R. Metl. Soc. 115, 941963.CrossRefGoogle Scholar
Shin, J. O., Dalziel, S. B. & Linden, P. F. 2004 Gravity currents produced by lock exchange. J. Fluid Mech. 521, 134.CrossRefGoogle Scholar
Sutherland, B. & Nault, J. 2007 Intrusive gravity currents propagating along thin and thick interfaces. J. Fluid Mech. 586, 109118.CrossRefGoogle Scholar
Sutherland, B. R., Flynn, M. R. & Dohan, K. 2004 Internal wave excitation from a collapsing mixed region. Deep Sea Res. II 51, 28892904.CrossRefGoogle Scholar
Sutherland, B. R., Kyba, P. J. & Flynn, M. R. 2004 Intrusive gravity currents in two-layer fluids. J. Fluid Mech. 514, 327353.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. 2006 Energy balances for propagating gravity currents: homogenous and stratified ambients. J. Fluid Mech. 565, 363380.CrossRefGoogle Scholar
Yih, C. S. 1965 Dynamics of Nonhomogenous Fluids. MacMillan.Google Scholar