Hostname: page-component-76d6cb85b7-f97m6 Total loading time: 0 Render date: 2026-07-13T22:55:29.236Z Has data issue: false hasContentIssue false
  • English
  • Français

The refraction of sea waves in shallow water

Published online by Cambridge University Press:  28 March 2006

M. S. Longuet-Higgins
M. S. Longuet-Higgins
Affiliation:
National Institute of Oceanography, Wormley
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper considers the changes that occur in the character of short-crested sea waves when they are refracted by a shallowing depth of water. Besides a change in mean wave-length and direction there is also a change (usually an increase) in the mean length of the crests. If the waves approach obliquely they become skew, that is, the crests become staggered one behind another.

When a short-crested sea is superposed on a long-creasted swell, refraction tends to amplify the longer waves more than the shorter ones. This also produces an increase in the mean length of the crests.

Numerical examples are given.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 1 , Issue 2 , July 1956 , pp. 163 - 176
Copyright
© 1956 Cambridge University Press

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

Barber, N. F. 1950 Ocean waves and swell. Lecture published by Institution of Civil Engineers, London.
Burnside, W. 1915 On the modification of a train of waves as it advances into shallow water, Proc. Lond. Math. Soc. (2), 14, 131.Google Scholar
Green, G. 1838 On the motion of waves in a variable canal of small depth and width, Trans. Camb. Phil. Soc., 6, 457.Google Scholar
Jeffreys, H. 1924 On water waves near the shore, Phil. Mag. (6), 48, 44.Google Scholar
Lamb, H. 1932 Hydrodynamics, 6th ed. Cambridge University Press.
Longuet-Higgins, M. S. 1956a The statistical analysis of a random moving surface, Phil. Trans. A (in press).Google Scholar
Longuet-Higgins, M. S. 1956b On the transformation of a continuous spectrum by refraction, Proc. Camb. Phil. Soc. (in press).Google Scholar
Stokes, G. G. 1847 On the theory of oscillatory waves, Trans. Camb. Phil. Soc. 8, 441. Mathematical and Physical Papers, 1, 197. Cambridge University Press.Google Scholar
Stoneley, R. 1935 The refraction of a wave group, Proc. Camb. Phil. Soc., 31, 360.Google Scholar
Ursell, F. 1953 The long-wave paradox in the theory of gravity waves, Proc. Camb. Phil. Soc., 49, 685.Google Scholar