An Experimental Study of the Statistical Properties of Wind-Generated Gravity Waves

  • Norden E. Huang
  • Steven R. Long
  • Larry F. Bliven


Statistical properties of wind-generated waves are studied under laboratory conditions. The properties studied include distributions of various zero crossings; crest, trough, and wave amplitudes; local maxima and minima; group length and number of waves per group; and the joint probability distribution of amplitude and period. The results indicate that all the distribution functions are in qualitative agreement with the theoretical expressions derived by Longuet-Higgins in the late 1950s and early 1960s; however, systematic deviations from the results based on a joint Gaussian distribution are apparent. The most likely dynamical reasons for the deviations are: the nonlinear mechanism causing the unsymmetric crest and trough shape, and the breaking of waves. Both of these reasons for deviations are found to be controlled by a single internal variable, the significant slope, defined as the ratio of the rms wave height to the wavelength corresponding to the waves at the spectral peak. The significant slope is also found to be the controlling factor in determining the spectral shape and evolution. Thus, the present set of detailed observational data could be used as the base to link the dynamics and the statistical properties of the wind wave field.


Wave Field Wind Wave Joint Probability Distribution Fourth Moment Group Length 
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  1. Benjamin, T. B., and J. E. Feir (1967): The disintegration of wave trains on deep water. Part I. Theory. J. Fluid Meek 27, 417–430.MATHCrossRefGoogle Scholar
  2. Cartwright, D. E., and M. S. Longuet-Higgins (1956): The statistical distribution of the maxima of a random function. Proc. R. Soc. London Ser. A 237, 212–232.MathSciNetMATHCrossRefGoogle Scholar
  3. Ewing, J. A. (1973): Mean length of runs of high waves. J. Geophys. Res. 78, 1933–1936.CrossRefGoogle Scholar
  4. Favre, A., and K. Hasselmann (eds.) (1978): Turbulent Fluxes Through the Sea Surface, Wave Dynamics, and Prediction, Plenum Press, New York.Google Scholar
  5. Goda, Y. (1970): Numerical experiments on wave statistics with spectral simulation. Rep. Port Harbor Res. Inst., Min. Transport, Yokosuka 9.Google Scholar
  6. Hasselmann, K., D. B. Ross, P. Müller, and W. Sell (1976): A parametric wave prediction model. J. Phys. Oceanogr. 6, 200–228.CrossRefGoogle Scholar
  7. Houmb, O. G., B. Pedersen, and P. Steinbakke (1974): Norwegian wave climate study. Sym. Ocean Wave Measurement and Analysis 1, 25–39.Google Scholar
  8. Huang, N. E., and S. R. Long (1980): An experimental study of the surface elevation probability distribution and statistics of wind generated waves. J. Fluid Meek 101, 179–200.CrossRefGoogle Scholar
  9. Huang, N. E., S. R. Long, C. C. Tung, Y. Yuen, and L. F. Bliven (1981a): A unified two-parameter wave spectral model for a general sea state. J. Fluid Meek 112, 203–224.MATHCrossRefGoogle Scholar
  10. Huang, N. E., S. R. Long, and L. F. Bliven (1981b): On the importance of the significant slope in empirical wind wave studies. J. Phys. Oceanogr. 11, 509–573.Google Scholar
  11. Lake, B. M., and H. C. Yuen (1977): A note on some nonlinear water-wave experiments and the comparison of data with theory. J. Fluid Meek 83, 75–81.CrossRefGoogle Scholar
  12. Lake, B. M., and H. C. Yuen (1978): A new model for nonlinear wind waves. Part 1. Physical model and experimental evidence. J. Fluid Meek 88, 33–62.MATHCrossRefGoogle Scholar
  13. Longuet-Higgins, M. S. (1952): On the statistical distribution of the height of sea waves. J. Mar. Res. 11, 245–266.Google Scholar
  14. Longuet-Higgins, M. S. (1956): Statistical properties of a moving waveform. Proc. Cambridge Philos. Soc. 52, 234–245.MathSciNetMATHCrossRefGoogle Scholar
  15. Longuet-Higgins, M. S. (1957): The statistical analysis of a random moving surface. Philos. Trans. R. Soc. London Ser. A 249, 321–387.MathSciNetMATHCrossRefGoogle Scholar
  16. Longuet-Higgins, M. S. (1958): On the intervals between successive zeros of a random function. Proc. R. Soc. London Ser. A 246, 99–118.MathSciNetMATHCrossRefGoogle Scholar
  17. Longuet-Higgins, M. S. (1962): The statistical geometry of random surfaces. Proc. 13th Symp. Appl. Math. 13, 105–143.Google Scholar
  18. Longuet-Higgins, M. S. (1963): The effect of non-linearities on statistical distributions in the theory of sea waves. J. Fluid Meek 17, 459–480.MathSciNetMATHCrossRefGoogle Scholar
  19. Longuet-Higgins, M. S. (1969): On wave breaking and the equilibrium spectrum of wind-generating waves. Proc. R. Soc. London Ser. A 310, 151–159.CrossRefGoogle Scholar
  20. Longuet-Higgins, M. S. (1975): On the joint distribution of the periods and amplitudes of sea waves. J. Geophys. Res. 80, 2688–2694.CrossRefGoogle Scholar
  21. Longuet-Higgins, M. S. (1980a): On the distribution of the heights of sea waves: Some effect of nonlinearity and finite bandwidth. J. Geophys. Res. 88, 1519–1523.CrossRefGoogle Scholar
  22. Longuet-Higgins, M. S. (1980b): Modulation of the amplitude of steep wind waves. J. Fluid Meek 99, 705–713.MathSciNetCrossRefGoogle Scholar
  23. Longuet-Higgins, M. S., and E. D. Cokelet (1976): The deformation of steep surface waves on water. L A numerical method of computation. Proc. R. Soc. London Ser. A 350, 1–26.MathSciNetMATHCrossRefGoogle Scholar
  24. Pierson, W. J., and L. Moskowitz (1964): A proposed spectral form for fully developed wind sea based on the similarity theory of S. A. Kitaigorodskii. J. Geophys. Res. 69, 5181–5190.CrossRefGoogle Scholar
  25. Rice, S. O. (1944): The mathematical analysis of random noise. Bell Syst. Tech. J. 23, 282–332.MathSciNetMATHGoogle Scholar
  26. Rice, S. O. (1945): The mathematical analysis of random noise. Bell Syst. Tech. J 24, 46–156.MathSciNetMATHGoogle Scholar
  27. Sturm, G. V., and F. Y. Sorrell (1973): Optical wave measurement technique and experimental comparison with wave height probes. Appl. Opt. 12, 1228–1233.CrossRefGoogle Scholar
  28. Tayfun, M. A. (1980b): Narrow-band nonlinear sea waves. J. Geophys. Res. 85, 1548–1552.CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1986

Authors and Affiliations

  • Norden E. Huang
    • 1
  • Steven R. Long
    • 2
  • Larry F. Bliven
    • 3
  1. 1.NASA Goddard Space Flight CenterGreenbeltUSA
  2. 2.Wallops Flight CenterNASA Goddard Space Flight CenterWallops IslandUSA
  3. 3.Oceanic Hydrodynamics, Inc.SalisburyUSA

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