Hostname: page-component-cb9f654ff-mnl9s Total loading time: 0 Render date: 2025-08-14T02:19:10.837Z Has data issue: false hasContentIssue false
  • English
  • Français

Long waves in running water

Published online by Cambridge University Press:  24 October 2008

J. C. Burns
J. C. Burns
Affiliation:
Department of MathematicsUniversity of Manchester
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.

Classical shallow-water theory for the propagation of long waves in running water is modified by the inclusion of the effects of the vorticity present in the main stream as the result of the action of viscosity. When this vorticity is assumed constant, a non-linear theory can be used, but for more general velocity distributions in the main stream it is necessary to linearize the problem.

In the linearized theory, a general equation is obtained connecting the wave velocity with the velocity in the undisturbed stream and this is solved in several special cases. It is shown generally that the wave velocity relative to the mean flow is always greater than the value given by the classical theory. The wave velocity relative to the bottom of the stream has two values, one less than the minimum stream velocity and the other greater than the maximum stream velocity.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 49 , Issue 4 , October 1953 , pp. 695 - 706
Copyright
Copyright © Cambridge Philosophical Society 1953

References

(1)Biésel, F.Étude théorique de la houle en eau courante. Houille blanche, 5 (1950), 279–85.CrossRefGoogle Scholar
(2)Coulson, C. A.Waves, 3rd ed. (Edinburgh, 1944).Google Scholar
(3)Lamb, H.Hydrodynamics, 6th ed. (Cambridge, 1932).Google Scholar
(4)Stokes, G. G.Trans. Camb. phil. Soc. 8 (1847), 441Google Scholar
Stokes, G. G.Collected papers, vol. 1 (Cambridge, 1880), p. 197.Google Scholar
(5)Thompson, P. D.The propagation of small surface disturbances through rotational flow. Ann. N.Y. Acad. Sci. 51 (1949), 463–74.CrossRefGoogle Scholar