Effects of empirical dissipation terms in the solution of the undular bore
Author:
John G. B. Byatt-Smith
Journal:
Quart. Appl. Math. 28 (1971), 499-515
DOI:
https://doi.org/10.1090/qam/99773
MathSciNet review:
QAM99773
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Abstract |
References |
Additional Information
Abstract: In this paper we consider the problem of a steady bore running downhill. The effects of dissipation are included empirically, using the Chézy law. The method of solution is based on an averaging technique which assumes that the uniform solution is slowly varying.
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G. B. Airy, “Tides and waves,” in Encyclopaedia metropolitana, London (1845)
T. B. Benjamin and M. J. Lighthill, On cnoidal waves and bores, Proc. Roy. Soc. London Ser. A224, 448–460 (1954)
J. Boussinesq, Essai sur la théorie des eaux courants, Mém. Pres. Acad. Sci. Paris 23 (1877)
W. Chester, Proc. Roy. Soc. London Ser. A 306, 5 (1968)
R. F. Dressler, Mathematical solution of the problem of roll-waves in inclined open channels, Comm. Pure Appl. Math. 2, 149–194 (1949)
H. Favre, Etude théorique et experimentale des ondes de translation dans les canaux découvents, Dunod, Paris, 1935
G. H. Keulegan and G. W. Patterson, Mathematical theory of irrotational translation waves, J. Research Nat. Bur. Standards 24, 47–101 (1940)
D. J. Korteweg and G. De Vries, Philos. Mag. (5) 39, 422 (1895)
R. Lemoine, Sur les ondes positives de translation dans les canaux et sur le ressaut ondule de faible amplitude, La Houille Blanch 2, Grenoble, France (1948)
M. J. Lighthill and G. B. Whitham, On kinematic waves. I: Flood movement in long rivers, Proc. Roy. Soc. London Ser. A 229, 281–316 (1955)
Lord Rayleigh, Philos. Mag. (5) 1, 247 (1876); Proc. Roy. Soc. London Ser. A 90, 344 (1914)
S. J. Russell, Rep. Brit. Assn. 417 (1837) Rep. Brit. Assn. p. 311 (1844)
J. A. Sandover and T. D. Taylor, Experiments on surge waves, Water Power 9, 418 (1957)
J. A. Sandover and O. C. Zienkiewicz, La Houille Blanch 17, 443, Grenoble, France (1962)
H. A. Thomas, Hydraulics of flood movement in rivers, Carnegie Institute of Technology, Pittsburg, 1937
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Article copyright:
© Copyright 1971
American Mathematical Society
