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Calculations of the development of an undular bore

Published online by Cambridge University Press:  28 March 2006

D. H. Peregrine
D. H. Peregrine
Affiliation:
Department of Mathematics, University of Bristol
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Abstract

If a long wave of elevation travels in shallow water it steepens and forms a bore. The bore is undular if the change in surface elevation of the wave is less than 0·28 of the original depth of water. This paper describes the growth of an undular bore from a long wave which forms a gentle transition between a uniform flow and still water. A physical account of its development is followed by the results of numerical calculations. These use finite-difference approximations to the partial differential equations of motion. The equations of motion are of the same order of approximation as is necessary to derive the solitary wave. The results are in general agreement with the available experimental measurements.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 25 , Issue 2 , June 1966 , pp. 321 - 330
Copyright
© 1966 Cambridge University Press

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References

Benjamin, T. B. & Lighthill, M. J. 1954 On cnoidal waves and bores. Proc. Roy. Soc., A 224, 448–60.Google Scholar
Binnie, A. M. & Orkney, J. C. 1955 Experiments on the flow of water from a reservoir through an open channel. II. The formation of hydraulic jumps. Proc. Roy. Soc., A 230, 237–46.Google Scholar
Broer, L. J. F. 1964 Appl. Sci. Res., B 11, 273–85.
Favre, H. 1935 Ondes de Translation. Paris: Dunod.
Keulegan, G. H. & Patterson, G. W. 1940 Mathematical theory of irrotational translation waves. Nat. Bur. Standards J. Res. 24, 47–101.Google Scholar
Korteweg, D. J. & de Vries, G. 1895 Phil. Mag. (V), 39, 422–43.
Long, R. R. 1964 J. Fluid Mech. 20, 161–70.
Sandover, J. A. & Taylor, C. 1962 La Houille Blanche, 17, 443–55.
Sandover, J. A. & Zienkiewicz, O. C. 1957 Experiments on surge waves. Water Power, 9, 418–24.Google Scholar
Stoker, J. J. 1957 Water Waves. New York: Interscience.