Gravity‐Current Fronts Advancing into Horizontal Ambient Flow
Publication: Journal of Hydraulic Engineering
Volume 119, Issue 3
Abstract
An integral model of the front of a gravity current advancing into flowing receiving fluid of slightly smaller density is presented. The analysis is an extension of that given by Benjamin in 1968 in that boundary‐layer shear and energy losses related to front propagation and ambient flow are taken into account. The number of empirical coefficients involved is reduced by requiring that the front speed relative to the receiving flow decreases with increasing flow rate of the receiving fluid, and that for zero front height in counterflow, the solution agrees with the case of the tip of an arrested density wedge. The single remaining empirical coefficient in the expression for the front speed is adopted from earlier work on lock exchange flow. The maximal height of realizable fronts, which is known to be limited to a certain fraction of the water depth, is shown to increase with the ambient velocity. Satisfactory agreement is obtained with experimental results on counterflows as well as coflows reported in the literature.
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References
1.
Baines, W. D., Rottman, J. W., and Simpson, J. E. (1985). “The motion of constant‐volume air cavities in long horizontal tubes.” J. Fluid Mech., 161, 313–327.
2.
Barr, D. I. H. (1963). “Densimetric exchange flow in rectangular channels.” La Houille Blanche, 18(7), 739–766.
3.
Benjamin, T. B. (1968). “Gravity currents and related phenomena.” J. Fluid Mech., 31(2), 209–248.
4.
Britter, R. E., and Simpson, J. E. (1978). “Experiments on the dynamics of a gravity current head.” J. Fluid Mech., 88(2), 223–240.
5.
Bühler, J., Wright, S. J., and Kim, Y. (1991). “Gravity currents advancing into a coflowing fluid.” J. Hydraul. Res., 29(2), 243–257.
6.
Denton, R. A. (1985). “Density current inflows to run of the river reservoirs.” Proc., 21st Congress IAHR, Melbourne, Australia, 2, 243–247.
7.
Jirka, G. H., and Arita, M. (1987). “Density currents or density wedges: Boundary‐layer influence and control methods.” J. Fluid Mech., 177, 187–206.
8.
Kranenburg, C. (1978). “Internal fronts in two‐layer flow.” J. Hydr. Div., ASCE, 104(10), 1449–1453.
9.
Kranenburg, C. (1993). “Unsteady gravity currents advancing along a horizontal surface.” J. Hydraul. Res. (in press).
10.
Schijf, J. B., and Schönfeld, J. C. (1953). “Theoretical considerations on the motion of salt and fresh water.” Proc., Minnesota Int. Hydr. Conv., IAHR, ASCE, 321–333.
11.
Simpson, J. E., and Britter, R. E. (1979). “The dynamics of the head of a gravity current advancing over a horizontal surface.” J. Fluid Mech., 94(3), 477–495.
12.
Simpson, J. E., and Britter, R. E. (1980). “A laboratory model of an atmospheric mesofront.” Quarterly Journal of the Royal Meterological Society, Bracknell, England, 106, 485–500.
13.
Wilkinson, D. L. (1972). “Dynamics of contained oil slicks.” J. Hydr. Div., ASCE, 98(6), 1013–1030.
14.
Wilkinson, D. L. (1982). “Motion of air cavities in long horizontal ducts.” J. Fluid Mech., 118, 109–122.
15.
Wright, S. J. (1986). “Aspects of far‐field control on buoyant jet mixing.” Rep. No. 24‐86, Inst. of Hydromech., Federal Inst. of Tech., Zürich, Switzerland.
16.
Wright, S. J., Kim, Y., and Bühler, J. (1987). “Controls on density current propagation.” Preprints 3rd Int. Conf. on Strat. Flows, Calif. Inst. of Techn., Pasadena, Calif., 1, B3.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 119 • Issue 3 • March 1993
Pages: 369 - 379
Copyright
Copyright © 1993 American Society of Civil Engineers.
History
Received: Oct 17, 1991
Published online: Mar 1, 1993
Published in print: Mar 1993
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