Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-05T13:08:42.373Z Has data issue: false hasContentIssue false

An investigation of internal solitary waves in a two-fluid system

Published online by Cambridge University Press:  20 April 2006

C. Gary Koop
Affiliation:
Fluid Mechanics Department, TRW/DSSG, One Space Park, Redondo Beach, California 90278
Gerald Butler
Affiliation:
Fluid Mechanics Department, TRW/DSSG, One Space Park, Redondo Beach, California 90278

Abstract

The results of an experimental investigation dealing with finite-amplitude internal solitary waves in a two-fluid system are presented. Particular attention is paid to characterizing solitons in terms of their shape and amplitude–wavelength scale relationship. Two cases are considered, viz., a shallow- and a deep-water configuration, in order to study the depth effect upon the propagational characteristics of the waves. Comparisons are made between the experimental results and existing internal-wave theories. In addition, discussion is presented describing how these existing theories may be extended to include higher-order nonlinear and viscous effects.

Type
Research Article
Copyright
© 1981 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

Benjamin, T. B. 1966 Internal waves of finite amplitude and permanent form. J. Fluid Mech. 25, 241.Google Scholar
Benjamin, T. B. 1967 Internal waves of permanent form in fluids of great depth. J. Fluid Mech. 25, 559.Google Scholar
Benney, C. J. 1966 Long nonlinear waves in fluid flows. J. Math. Phys. 45, 52.Google Scholar
Chen, H. H., Lee, Y. C. & Pereira, N. R. 1979 Algebraic internal wave solitons and the integrable Calogero — Moser — Sutherland N-body problem. Phys. Fluids 22, 187.Google Scholar
Christie, D. R., Muirhead, K. & Hales, A. 1978 On solitary waves in the atmosphere. J. Atm. Sci. 35, 805.Google Scholar
Davis, R. E. & Acrivos, A. 1967 Solitary internal waves in deep water. J. Fluid Mech. 29, 593.Google Scholar
Fornberg, B. E. 1977 On a Fourier method for the integration of hyperbolic equations. SIAM J. Numerical Analysis 12, 509.Google Scholar
Hammack, J., Leone, C. & Segur, H. 1981 Long internal waves. (To be published.)
Hammack, J. L. & Segur, H. 1974 The Korteweg — de Vries equation and water waves. Part 2. Comparison and experiments. J. Fluid Mech. 65, 289.Google Scholar
Joseph, R. I. 1977 Solitary waves in a finite depth fluid. J. Phys. A, Math. General 10, L225.Google Scholar
Kao, T. & Pao, H. P. 1979 Wake collapse in the thermocline and internal solitary waves. J. Fluid Mech. 97, 115.Google Scholar
Kakutani, T. & Matsuuchi, K. 1975 Effect of viscosity on long gravity waves. J. Phys. Soc. Japan 39, 237.Google Scholar
Keulegan, G. H. 1948 Gradual damping of solitary waves. N.B.S. J. 40, 480.Google Scholar
Kubota, T., Ko, D. R. S. & Dobbs, L. D. 1978 Propagation of weakly nonlinear internal waves in a stratified fluid of finite depth. A.I.A.A. J. Hydronautics 12, 157.Google Scholar
Lake, B. M., Yuen, H. C., Rungaldier, H. & Ferguson, W. 1977 Nonlinear deep-water waves: theory and experiment. Part 2. Evolution of a continuous wave train. J. Fluid Mech. 83, 49.Google Scholar
Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.
Matsuuchi, K. 1976 Numerical investigations on long gravity waves under the influence of viscosity. J. Phys. Soc. Japan 41, 681.Google Scholar
Meiss, J. D. & Pereira, N. R. 1978 Internal wave solitons. Phys. Fluids 21, 700.Google Scholar
Ono, H. 1975 Algebraic solitary waves in stratified fluids. J. Phys. Soc. Japan 39, 1082.Google Scholar
Osborne, A., Burch, T. & Scarlet, R. 1978 The influence of internal waves on deep water drilling. J. Petroleum Tech. 1497.Google Scholar
Osborne, A. & Burch, T. 1980 Internal solitons in the Andaman Sea. Science (submitted).
Segur, H. 1973 The Korteweg — de Vries equation and water waves. Solutions of the equations. Part 1. J. Fluid Mech. 59, 721.Google Scholar
Walker, L. R. 1973 Interfacial solitary waves in a two fluid medium. Phys. Fluids 16, 1796.Google Scholar
Yates, C. 1978 An experimental study of internal solitary waves. AIAA 16th Aerospace Sciences Meeting, Huntsville, Alabama, Paper no. 78–262.