Hostname: page-component-cb9f654ff-qc88w Total loading time: 0 Render date: 2025-08-22T06:02:31.900Z Has data issue: false hasContentIssue false
  • English
  • Français

Surface and internal waves in a liquid of variable depth

Published online by Cambridge University Press:  17 April 2009

D. G. Hurley  and
J. Imberger
D. G. Hurley
Affiliation:
Department of Mathematics, University of Western Australia, Nedlands. Western Australia.
J. Imberger
Affiliation:
Department of Mathematics, University of Western Australia, Nedlands. Western Australia.
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.

Consider a stably stratified liquid, whose density varies exponentially with the vertical co-ordinate, that is bounded above by a free surface and below by a bed whose height depends on only one of the horizontal co-ordinates. Suppose that a gravity wave, that may be either a surface or an internal one, is travelling in a direction normal to the lines of constant depth. It is shown that if the frequency is below a certain value an infinite number of waves, all of the same frequency but having differing wave lengths, are generated and expressions for their amplitude are given in terms of the changes in depth which are assumed to be small.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 1 , Issue 1 , April 1969 , pp. 29 - 46
Copyright
Copyright © Australian Mathematical Society 1969

References

[1] Cox, C.S. and Sandstrom, H., “Coupling of internal and surface waves in water of variable depth”, J. Ocean. Soc. Japan, 20th Annivers. Vol. (1962), 499–513.Google Scholar
[2] Lamb, Horace, Hydrodynamics, (Cambridge University Press, Sixth Edition, 1932).Google Scholar
[3] Mowbray, D.E. and Rarity, B.S.H., “A theoretical and experimental investigation of the phase configuration of internal waves of small amplitude in a density stratified liquid”, J. Fluid Mech. 28 (1967), 1–16.CrossRefGoogle Scholar
[4] Lighthill, M.J., Fourier analysis and generalized functions, (Cambridge University Press, 1962).Google Scholar
[5] Faddeyeva, V.N. and Terent'ev, N.M., Tables of the probability integral for complex argument (Pergamon, Oxford, 1961).Google Scholar
[6] Schelkunoff, S.A., “Remarks concerning wave propogation in stratified media”, Comm. Pure Appl. Math. 4 (1951), 117–128.CrossRefGoogle Scholar