Hostname: page-component-7479d7b7d-jwnkl Total loading time: 0 Render date: 2024-07-12T19:03:28.529Z Has data issue: false hasContentIssue false
  • English
  • Français

Progressive internal waves on slopes

Published online by Cambridge University Press:  28 March 2006

Carl Wunsch
Carl Wunsch
Affiliation:
Department of Geology and Geophysics, Massachusetts Institute of Technology, Cambridge, Massachusetts
Get access Rights & Permissions [Opens in a new window]

Abstract

The refraction of progressive internal waves on sloping bottoms is treated for the case of constant Brunt—Väisälä frequency. In two dimensions simple, explicit expressions for the changing wavelengths and amplitudes are found. For small slopes, the solutions reduce to simple propagating waves at infinity.

The singularity along a characteristic is shown to be removable, though the solutions are now inhomogeneous waves. The viscous boundary layers of the wedge geometry are briefly considered with the inviscid solutions remaining as interior solutions.

A theory valid for small slopes is obtained for three-dimensional waves. The waves are refracted in the usual manner, turning parallel to the beach in shallow water.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 35 , Issue 1 , 16 January 1969 , pp. 131 - 144
Copyright
© 1969 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

Gaul, R. D. 1961 Observations of internal waves near Hudson Canyon J. Geophys. Res. 66, 3821–30.Google Scholar
Greenspan, H. P. 1963 A string problem J. of Math. Analys. Applic. 6, 339–48.Google Scholar
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
Lee, O. S. 1961 Observations of internal waves in shallow water Limnol. Oceanogr. 6, 312–21.Google Scholar
Magaard, L. 1962 Zur berechnung interner wellen in Meeresräumen mit nichtebenen Böden bei einer spezellien Diehterer teilung Kieler Meeresforsch, 18, 161–83.Google Scholar
Phillips, O. M. 1966 The Dynamics of the Upper Ocean. Cambridge University Press.
Sandstrom, H. 1966 On the importance of topography in generation and propagation of internal waves. Ph.D. Thesis, Univ. of California at San Diego.
Wunsch, C. 1968 On the propagation of internal waves up a slope Deep-Sea Res. 25, 251–258.Google Scholar