Hostname: page-component-848d4c4894-m9kch Total loading time: 0 Render date: 2024-04-30T10:24:54.872Z Has data issue: false hasContentIssue false
  • English
  • Français

Surface waves on water of non-uniform depth

Published online by Cambridge University Press:  28 March 2006

Joseph B. Keller
Joseph B. Keller
Affiliation:
Institute of Mathematical Sciences, New York University
Get access Rights & Permissions [Opens in a new window]

Extract

Gravity waves occur on the surface of a liquid such as water, and the manner in which they propagate depends upon its depth. Although this dependence is described in principle by the equations of the ‘exact linear theory’ of surface waves, these equations have not been solved except in some special cases. Therefore, oceanographers have been unable to use the theory to describe surface wave propagation in water whose depth varies in a general way. Instead they have employed a simplified geometrical optics theory for this purpose (see, for example, Sverdrup & Munk (1944)). It has been used very successfully, and consequently various attempts, only partially successful, have been made to deduce it from the exact linear theory. It is the purpose of this article to present a derivation which appears to be satisfactory and which also yields corrections to the geometrical optics theory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 4 , Issue 6 , November 1958 , pp. 607 - 614
Copyright
© 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.)

References

Friedrichs, K. O. 1948 Water waves on a shallow sloping beach, Comm. Pure Appl. Math., 1, 109–134.Google Scholar
Kay, I. & Keller, J. B. 1954 Asymptotic evaluation of the field at a caustic, J. Appl. Phys., 25, 876–883.Google Scholar
Lowell, S. C. 1949 The propagation of waves in shallow water, Comm. Pure Appl. Math., 2, 275–291.Google Scholar
Luneburg, R. K. 1944 Mathematical theory of optics, Brown University Lecture Notes.
Miche, A. 1944 Mouvements ondulatories de la mer en profondeur constante ou décroissante, Annales des ponts et chaussées 14, 131–164, 270–292, 369–406.Google Scholar
Peters, A. S. 1952 Water waves over sloping beaches, Comm. Pure Appl. Math., 5, 87–108.Google Scholar
Stoker, J. J. 1947 Surface waves in water of variable depth, Quart. Appl. Math., 5, 1–54.Google Scholar
Sverdrup, H. U. & Munk, W. H. 1944 Breakers and surf, U.S. Navy Department, Hydrographic Office, Publ. no. 234.