Hostname: page-component-76c49bb84f-zv2rg Total loading time: 0 Render date: 2025-07-13T05:19:33.846Z Has data issue: false hasContentIssue false
  • English
  • Français

Experiments on nonlinear instabilities and evolution of steep gravity-wave trains

Published online by Cambridge University Press:  20 April 2006

Ming-Yang Su ,
Mark Bergin ,
Paul Marler  and
Richard Myrick
Ming-Yang Su
Affiliation:
Naval Ocean Research and Development Activity, NSTL Station. Mississippi 39529
Mark Bergin
Affiliation:
Naval Ocean Research and Development Activity, NSTL Station. Mississippi 39529
Paul Marler
Affiliation:
Naval Ocean Research and Development Activity, NSTL Station. Mississippi 39529
Richard Myrick
Affiliation:
Naval Ocean Research and Development Activity, NSTL Station. Mississippi 39529
Get access Rights & Permissions [Opens in a new window]

Abstract

A series of experiments on strong nonlinear instabilities of gravity-wave trains of large steepness 0·25 ≤ ak ≤ 0·34 in deep water in a long tow tank and a wide basin were performed. These experiments clarified several phenomena such as subharmonic instabilities, wave breaking, evolution of power spectra and directional energy spreading. It was found that an initial two-dimensional wavetrain of large steepness evolved into a series of three-dimensional spilling breakers, and was followed by a transition to a two-dimensional modulated wave train during which a series of oblique wave groups were radiated. The final stage of evolution was a series of modulated, two-dimensional wave groups with lower steepness and frequency. The three most frequent normal modes of two-dimensional subharmonic instabilities underlying the frequency downshifting, in the order of their relative occurrence, are found to be about 4/3, 5/4 and 3/2 in terms of the ratio of the fundamental to perturbed wave frequencies. The Bimescale for the phenomenon of the frequency downshifting is from 40 to 60 fundamental wave periods. Comparisons of the experimental results with existing theories showed that observed processes have several qualitative similarities with theoretical computations.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 124 , November 1982 , pp. 45 - 72
Copyright
© 1982 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.)

Article purchase

Temporarily unavailable

References

Benjamin, T. B. & Feir, J. E. 1967 The disintegration of wave trains on deep water. Part 1. Theory. J. Fluid Mech. 27, 417–430.Google Scholar
Hsu, Y.-H. L. 1976 A linear capacitance meter with applications to water wave measurements. Unpublished report, College of Marine Studies, University of Delaware, Newark, Delaware.
Lake, B. M., Yuen, H. C., Rungaldier, H. & Ferguson, W. E. 1977 Nonlinear deep-water waves: theory and experiment. Part 2. Evolution of a continuous wave train. J. Fluid Mech. 83, 49–74.Google Scholar
Longuet-Higgins, M. S. 1978a The instabilities of gravity waves of finite amplitude in deep water. I. Superharmonics. Proc. R. Soc. Lond. A 360, 417–458.Google Scholar
Longuet-Higgins, M. S. 1978b The instability of gravity waves of finite amplitude in deep water. II. Subharmonics. Proc. R. Soc. Lond. A 360, 489–505.Google Scholar
Longuet-Higgins, M. S. 1980 Modulation of the amplitude of steep wind waves. J. Fluid Mech. 99, 705–713.Google Scholar
Longuet-Higgins, M. S. & Cokelet, E. D. 1976 The deformation of deep surface waves on water. I. A numerical method of computation. Proc. R. Soc. Lond. A 350, 1–36.Google Scholar
Longuet-Higgins, M. S. & Cokelet, E. D. 1978 The deformation of deep surface waves on water. II. Growth of normal-mode instabilities. Proc. R. Soc. Lond. A 364, 1–28.Google Scholar
Mclean, J. W. 1982a Instabilities of finite-amplitude water waves. J. Fluid Mech. 114, 315–330.Google Scholar
Mclean, J. W. 1982b Instabilities of finite-amplitude gravity waves on water of finite depth. J. Fluid Mech. 114, 331–341.Google Scholar
Mclean, J. W., Ma, Y. C., Martin, D. U., Saffman, P. G. & Yuen, H. C. 1981 Three-dimensional instability of finite amplitude water waves. Phys. Rev. Lett. 46, 817–820.Google Scholar
Meiron, D. I., Saffman, P. G. & Yuen, H. C. 1982 Calculation of steady three-dimensional deep-water waves. J. Fluid Mech. 124, 109–121.Google Scholar
Su, M.-Y. 1982 Three-dimensional deep-water waves. Part 1. Experimental measurement of skew and symmetric wave patterns. J. Fluid Mech. 124, 73–108.Google Scholar
Yuen, H. C. & Lake, B. M. 1975 Nonlinear deep-water waves: Theory and experiment. Phys. Fluids 18, 956–960.Google Scholar
Yuen, H. C. & Lake, B. M. 1980 Instabilities of waves on deep water. Ann. Rev. Fluid Mech. 12, 303–334.Google Scholar