Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-22T19:52:11.009Z Has data issue: false hasContentIssue false
  • English
  • Français

An open-channel flow meeting a barrier and forming one or two jets

Published online by Cambridge University Press:  17 February 2009

L. H. Wiryanto  and
E. O. Tuck
L. H. Wiryanto
Affiliation:
Applied Mathematics Department, The University of Adelaide, Adelaide, 5005, Australia.
E. O. Tuck
Affiliation:
Applied Mathematics Department, The University of Adelaide, Adelaide, 5005, Australia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A steady two-dimensional free-surface flow in a channel of finite depth is considered. The channel ends abruptly with a barrier in the form of a vertical wall of finite height. Hence the stream, which is uniform far upstream, is forced to go upward and then falls under the effect of gravity. A configuration is examined where the rising stream splits into two jets, one falling backward and the other forward over the wall, in a fountain-like manner. The backward-going jet is assumed to be removed without disturbing the incident stream. This problem is solved numerically by an integral-equation method. Solutions are obtained for various values of a parameter measuring the fraction of the total incoming flux that goes into the forward jet. The limit where this fraction is one is also examined, the water then all passing over the wall, with a 120° corner stagnation point on the upper free surface.

Type
Research Article
Information
The ANZIAM Journal , Volume 41 , Issue 4 , April 2000 , pp. 458 - 472
Copyright
Copyright © Australian Mathematical Society 2000

References

[1]Dias, F. and Christodoulides, P., “Ideal jets falling under gravity”, Phys. Fluids A 3 (1991) 1711–1717.Google Scholar
[2]Dias, F. and Tuck, E. O., “Weir flows and waterfalls”, J. Fluid Mech. 230 (1991) 525–539.Google Scholar
[3]Dias, F. and Tuck, E. O., “A steady breaking wave”, Phys. Fluids A 5 (1993) 277–279.CrossRefGoogle Scholar
[4]Dias, F. and Vanden-Broeck, J.-M., “Flows emerging from a nozzle and falling under gravity”, J. Fluid Mech. 213 (1990) 465–477.Google Scholar
[5]Goh, M. K. and Tuck, E. O., “Thick waterfalls from horizontal slots”, J. Engng. Maths. 19 (1985) 341–349.Google Scholar
[6]Tuck, E. O., “Efflux from a slit in a vertical wall”, J. Fluid Mech. 176 (1987) 253–264.CrossRefGoogle Scholar
[7]Vanden-Broeck, J.-M., “Two-dimensional jets aimed vertically upwards”, J. Austral. Math. Soc. Ser. B 34 (1993) 393–400.CrossRefGoogle Scholar
[8]Vanden-Broeck, J.-M. and Keller, J., “Weir flows”, J. Fluid Mech. 176 (1987) 283–293.Google Scholar
[9]Wiryanto, L. H. and Tuck, E. O., “A back-turning jet formed by a uniform shallow stream hitting a vertical wall”, in International Conference on Differential Equations, Inst. Tek. Bandung, Indonesia, October 1996 (eds. van Groesen, B. and Soewono, E.), (Kluwer, 1997) 371–379.Google Scholar
[10]Wiryanto, L. H. and Tuck, E. O., “A boundary-element solution of a free-surface flow in a blocked channel”, in 8th Computational Techniques and Applications Conference, Adelaide, September 1997 (eds. Noye, J., Teubner, M. and Gill, A.), (World Scientific, Singapore, 1998) 743–750.Google Scholar