Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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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.


References [Enhancements On Off] (What's this?)

  • [1] G. B. Airy, ``Tides and waves,'' in Encyclopaedia metropolitana, London (1845)
  • [2] T. B. Benjamin and M. J. Lighthill, On conoidal waves and bores, Proc. Roy. Soc. London. Ser. A. 224 (1954), 448–460. MR 0076526, https://doi.org/10.1098/rspa.1954.0172
  • [3] J. Boussinesq, Essai sur la théorie des eaux courants, Mém. Pres. Acad. Sci. Paris 23 (1877)
  • [4] W. Chester, Proc. Roy. Soc. London Ser. A 306, 5 (1968)
  • [5] Robert F. Dressler, Mathematical solution of the problem of roll-waves in inclined open channels, Comm. Pure Appl. Math. 2 (1949), 149–194. MR 0033717, https://doi.org/10.1002/cpa.3160020203
  • [6] H. Favre, Etude théorique et experimentale des ondes de translation dans les canaux découvents, Dunod, Paris, 1935
  • [7] Garbis H. Keulegan and George W. Patterson, Mathematical theory of irrotational translation waves, J. Research Nat. Bur. Standards 24 (1940), 47–101. MR 0001698
  • [8] D. J. Korteweg and G. De Vries, Philos. Mag. (5) 39, 422 (1895)
  • [9] 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)
  • [10] M. J. Lighthill and G. B. Whitham, On kinematic waves. I. Flood movement in long rivers, Proc. Roy. Soc. London. Ser. A. 229 (1955), 281–316. MR 0072605, https://doi.org/10.1098/rspa.1955.0088
  • [11] Lord Rayleigh, Philos. Mag. (5) 1, 247 (1876); Proc. Roy. Soc. London Ser. A 90, 344 (1914)
  • [12] S. J. Russell, Rep. Brit. Assn. 417 (1837) Rep. Brit. Assn. p. 311 (1844)
  • [13] J. A. Sandover and T. D. Taylor, Experiments on surge waves, Water Power 9, 418 (1957)
  • [14] J. A. Sandover and O. C. Zienkiewicz, La Houille Blanch 17, 443, Grenoble, France (1962)
  • [15] H. A. Thomas, Hydraulics of flood movement in rivers, Carnegie Institute of Technology, Pittsburg, 1937


Additional Information

DOI: https://doi.org/10.1090/qam/99773
Article copyright: © Copyright 1971 American Mathematical Society


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