Hostname: page-component-7dd5485656-jtdwj Total loading time: 0 Render date: 2025-10-29T23:07:13.231Z Has data issue: false hasContentIssue false
  • English
  • Français

Mass transport in gravity waves

Published online by Cambridge University Press:  24 October 2008

F. Ursell
F. Ursell
Affiliation:
Trinity CollegeCambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

A proof is given of the existence of a slow drift associated with the passage of gravity waves over the surface of a frictionless fluid when the wave motion is irrotational. The drift is in the direction of propagation and is greatest near the surface, decreasing steadily towards the bottom, where it may be negative if the fluid is of finite depth. The particle displacement due to a solitary wave has similar properties. The proof confirms the approximate calculations of Stokes (6) and extends the proof of Rayleigh applicable only to deep water.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 49 , Issue 1 , January 1953 , pp. 145 - 150
Copyright
Copyright © Cambridge Philosophical Society 1953

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.)

Article purchase

Temporarily unavailable

References

REFERENCES

(1)Bagnold, R. A.J. Instn civ. Engrs, 27 (1947), 457.Google Scholar
(2)Lamb, H.Hydrodynamics, 6th ed. (Cambridge, 1932).Google Scholar
(3)Littlewood, J. E.Theory of functions (Oxford, 1944).Google Scholar
(4)Longuet-Higgins, M. S.Proc. roy. Soc. A (in the press).Google Scholar
(5)Rayleigh, Lord. Phil. Mag. (5), 1 (1876), 271. (Scientific papers, vol. 1, Cambridge, 1899, p. 263.)Google Scholar
(6)Stokes, G. G.Trans. Camb. phil. Soc. 8 (1847), 441–55. (Mathematical and physical papers, vol. 1, Cambridge, 1880, pp. 197–229.)Google Scholar
(7)Stokes, G. G.Mathematical and physical papers, vol. 1, pp. 314–26.Google Scholar
(8)Stokes, G. G.Mathematical and physical papers, vol. 5, p. 157.Google Scholar
(9)Titchmarsh, E. C.Theory of Fourier integrals, 2nd ed. (Oxford, 1948).Google Scholar
(10)Ursell, F.Mon. Not. R. astr. Soc. geophys. Suppl. 6 (1950), 1–8.CrossRefGoogle Scholar
(11)Weinstein, A.Abh. math. Sem. hamburg. Univ. 6 (1928), 263–4.CrossRefGoogle Scholar