Hostname: page-component-76fb5796d-vvkck Total loading time: 0 Render date: 2024-04-26T03:20:10.210Z Has data issue: false hasContentIssue false
  • English
  • Français

The Froude number for solitary waves

Published online by Cambridge University Press:  14 November 2011

J. B. McLeod
J. B. McLeod
Affiliation:
Wadham College, Oxford University, Oxford
Get access Rights & Permissions [Opens in a new window]

Synopsis

The paper is concerned with the problem of a solitary wave moving with constant form and constant velocity c on the surface of an incompressible, inviscid fluid over a horizontal bottom. The motion is assumed to be two-dimensional and irrotational, and if h is the depth of the fluid at infinity and g the acceleration due to gravity, then the Froude number F is defined by

The result that F>1 has recently been proved by Amick and Toland by means of a long and complicated argument. Here we give a short and simple one.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 97 , 1984 , pp. 193 - 197
Copyright
Copyright © Royal Society of Edinburgh 1984

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Amick, C. J. and Toland, J. F.. On solitary water-waves of finite amplitude. Arch. Rational Mech. Anal. 76 (1981), 9–95.CrossRefGoogle Scholar
2Milne-Thomson, L. M.. Theoretical Hydrodynamics, 5th edn (London: Macmillan, 1968).CrossRefGoogle Scholar
3Starr, V. T.. Momentum and energy integrals for gravity waves of finite height. J. Mar. Res. 6 (1947), 175–193.Google Scholar
4Longuet-Higgins, M. S.. On the mass, momentum, energy, and circulation of a solitary wave. Proc. Roy. Soc. London Ser. A 337 (1974), 1–13.Google Scholar