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Nonlinear free-surface flows emerging from vessels and flows under a sluice gate

Published online by Cambridge University Press:  17 February 2009

J. Asavanant and
J.-M. Vanden-Broeck
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Abstract

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Steady two-dimensional flows in a domain bounded below by an infinite horizontal wall and above by a semi-infinite horizontal wall, a vertical wall and a free surface are considered. The fluid is assumed to be inviscid and incompressible, and gravity is taken into account. The problem is solved numerically by series truncation. It is shown that for a given length of the vertical wall, there are two families of solutions. One family is characterized by a continuous slope at the separation point and a limiting configuration with a stagnation point and a 120° angle corner at the separation point. The other family is characterized by a stagnation point and a 90° angle corner at the separation point. Flows under a sluice gate with and without a rigid lid approximation upstream are also considered.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 38 , Issue 1 , July 1996, pp. 63 - 86
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Benjamin, T. B., “On the flow in channels when rigid obstacles are placed in the stream”, J. Fluid Mech. 1 (1956) 227–248.CrossRefGoogle Scholar
[2]Benjamin, T. B., “Gravity currents and related phenomena”, J. Fluid Mech. 31 (1968) 209–248.CrossRefGoogle Scholar
[3]Binnie, A. M., “The flow of water under a sluice gate”, Quart. J. Mech. and Applied Math. 5 (1952) 395–414.CrossRefGoogle Scholar
[4]Budden, P. and Norbury, J., “Uniqueness of free-boundary flows under gravity”, Arch. Rat. Math. Anal. 78 (1982) 361–380.CrossRefGoogle Scholar
[5]Dagan, G. and Tulin, M. P., “Two-dimensional free-surface gravity flow past blunt bodies”, J. Fluid Mech. 51 (1972) 529–543.CrossRefGoogle Scholar
[6]Fangmeier, D. D. and Strelkoff, T. S., “Solution for gravity flow under a sluice gate”, J. Eng. Mech. 94 (1968) 153–176.Google Scholar
[7]Gurevich, M. I., The theory of jets in an ideal fluid, International Series of Monographs in Pure and Applied Mathematics, Vol. 93 (Pergamon Press, 1961).Google Scholar
[8]Lee, J. and Vanden-Broeck, J.-M., “Two-dimensional jets falling from funnels and nozzles”, Phys. Fluids A 5 (1993) 2454–2460.CrossRefGoogle Scholar
[9]Masliyah, J. H., Nandakumar, K., Hemphill, F. and Fung, L., “Body-fitted coordinates for flow under sluice gates”, J. Hydr. Eng. 111 (1985) 922–933.CrossRefGoogle Scholar
[10]Tayler, A. B., “Singularities at flow separation points”, Quart. Journ. Mech. and Applied Math. 26 (1973) 153–172.CrossRefGoogle Scholar
[11]Vanden-Broeck, J.-M., “Flow under a gate”, Phys. Fluids 29 (1986) 3148–3151.CrossRefGoogle Scholar
[12]Vanden-Broeck, J.-M. and Keller, J. B., “Weir flows”, J. Fluid Mech. 176 (1987) 283–293.CrossRefGoogle Scholar
[13]Vanden-Broeck, J.-M. and Keller, J. B., “Surfing on solitary waves”, J. Fluid Mech. 198 (1989) 115–125.CrossRefGoogle Scholar
[14]Vanden-Broeck, J.-M. and Tuck, E. O., “Flow near the intersection of a free surface with a vertical wall”, SIAM J. Appl. Math. 54 (1994) 1–13.CrossRefGoogle Scholar