Hostname: page-component-745bb68f8f-hvd4g Total loading time: 0 Render date: 2025-01-07T19:01:58.710Z Has data issue: false hasContentIssue false
  • English
  • Français

Solitary internal waves in deep water

Published online by Cambridge University Press:  28 March 2006

Russ E. Davis  and
Andreas Acrivos
Russ E. Davis
Affiliation:
Present address: Institute of Geophysics and Planetary Physics, University of California, La Jolla. Department of Chemical Engineering, Stanford University
Andreas Acrivos
Affiliation:
Department of Chemical Engineering, Stanford University
Get access Rights & Permissions [Opens in a new window]

Abstract

A new type of solitary wave motion in incompressible fluids of non-uniform density has been investigated experimentally and theoretically. If a fluid is stratified in such a manner that there are two layers of different density joined by a thin region in which the density varies continuously, this type of wave propagates along the density gradient region without change of shape. In contrast to previously known solitary waves, these disturbances can exist even if the fluid depth is infinite. The waves are described by an approximate solution of the inviscid equations of motion. The analysis, which is based on the assumption that the wavelength of the disturbance is large compared with the thickness, L, of the region in which the density is not constant, indicates that the propagation velocity, U, is characterized by the dimensionless group (gL/U2) In (ρ1/ρ2), where g is the gravitational acceleration and ρ is the density. The value of this group, which is dependent on the wave amplitude and the form of the density gradient, is of the order one. Experimentally determined propagation velocities and wave shapes serve to verify the theoretical model.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 29 , Issue 3 , 6 September 1967 , pp. 593 - 607
Copyright
© 1967 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

Batchelor, G. K. 1956 On steady laminar flow with closed streamlines at large Reynolds number J. Fluid Mech. 1, 177.Google Scholar
Benjamin, T. B. 1966 Internal waves of finite amplitude and permanent form J. Fluid Mech. 25, 241.Google Scholar
Benjamin, T. B. 1967 J. Fluid Mech. 29, 559.
Courant, R. & Hilbert, P. 1953 Methods of Mathematical Physics, 1. New York: Interscience.
Lapidus, L. 1962 Digital Computation for Chemical Engineers. New York: McGraw-Hill.
Long, R. R. 1953 Some aspects of the flow of stratified fluids. I. A theoretical investigation Tellus 5, 42.Google Scholar
Long, R. R. 1965 On the Boussinesq approximation and its role in the theory of internal waves Tellus 17, 46.Google Scholar
Pettersson, O. 1912 Climatic variations in historic and prehistoric time. Svenska Hydrog-Biol. Kromm. Skrifter 5.Google Scholar
Yih, C. S. 1960a Gravity waves in a stratified fluid J. Fluid Mech. 8, 481.Google Scholar
Yih, C. S. 1960b Exact solutions for steady two-dimensional flow of a stratified fluid J. Fluid Mech. 9, 161.Google Scholar