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Supercritical flow of an ideal fluid over a spillway

Published online by Cambridge University Press:  17 February 2009

I. L. Collings  and
R. Grimshaw
I. L. Collings
Affiliation:
Department of Mathematics, Deakin University, Geelong, Vic. 3220, Australia
R. Grimshaw
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Vic. 3052, Australia
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Abstract

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The irrotational flow of an incompressible, inviscid fluid over a spiliway is considered. The reciprocal ε of the Froude number is taken to be small and the method of matched asymptotic expansions is applied. The bed of the spillway is horizontal far upstream and makes an angle α with the horizontal far downstream. The inner expansion is valid upstream and over the spillway, but is invalid far downstream. The outer expansion which is valid downstream fails to satisfy the upstream conditions. Unknown constants in the outer expansion are determined by the matching and composite expansions obtained.

Type
Research Article
Information
The ANZIAM Journal , Volume 20 , Issue 2 , December 1977 , pp. 211 - 225
Copyright
Copyright © Australian Mathematical Society 1977

References

REFERENCES

[1]Ackerberg, R. C., “Potential flow of a film down an inclined plate”, J. Eng. Math. 5 (1971), 127–135.CrossRefGoogle Scholar
[2]Birkhoff, G. and Zarantonello, E. H., Jets, wakes and cavities (Academic Press, 1957).Google Scholar
[3]Budden, P. J. and Norbury, J., “Sluice-gate problems with gravity”, Math. Proc. Camb. Phil. Soc. 81 (1977), 157–175.CrossRefGoogle Scholar
[4]Clarke, N. S., “On two-dimensional inviscid flow in a waterfall”, J. Fluid Mech. 22 (1965), 359–369.CrossRefGoogle Scholar
[5]Collings, I. L., “Free surface flows under gravity” (M.A. Thesis, University of Melbourne, 1977).Google Scholar
[6]Gurevich, M. I., Theory of jets in ideal fluids (Academic Press, 1965).Google Scholar
[7]Keady, G., “The jet from a horizontal slot at large Froude number”, Proc. Camb. Phil. Soc. 73 (1973), 515–529.CrossRefGoogle Scholar
[8]Keady, G. and Norbury, J., “The jet from a horizontal slot under gravity”, Proc. Roy. Soc. A 344 (1975), 471–487.Google Scholar
[9]Van Dyke, M., Perturbation methods in fluid mechanics (Academic Press, 1964).Google Scholar