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A unified two-parameter wave spectral model for a general sea state

Published online by Cambridge University Press:  20 April 2006

Norden E. Huang ,
Steven R. Long ,
Chi-Chao Tung ,
Yeli Yuen  and
Larry F. Bliven
Norden E. Huang
Affiliation:
NASA Wallops Flight Center, Wallops Island, VA 23337
Steven R. Long
Affiliation:
NASA Wallops Flight Center, Wallops Island, VA 23337
Chi-Chao Tung
Affiliation:
North Carolina State University, Raleigh, NC 27650
Yeli Yuen
Affiliation:
North Carolina State University, Raleigh, NC 27650
Larry F. Bliven
Affiliation:
Oceanic Hydrodynamics, Inc., Salisbury, MD 21801
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Abstract

Based on theoretical analysis and laboratory data, we proposed a unified two-parameter wave spectral model as $\phi(n) = \frac{\beta g^2}{n^m n_0^{5-m}} {\rm exp} \left\{-\frac{m}{4}\left(\frac{n_0}{n}\right)^4\right\}$ with β and m as functions of the internal parameter, the significant slope η of the wave field which is defined as $\sect = \frac{(\overline{\zeta^2})^{\frac{}1{2}}}{\lambda_0},$ where $\overline{\zeta^2}$ is the mean squared surface elevation, and λ0, n0 are the wavelength and frequency of the waves at the spectral peak. This spectral model is independent of local wind. Because the spectral model depends only on internal parameters, it contains information about fluid-dynamical processes. For example, it maintains a variable bandwidth as a function of the significant slope which measures the nonlinearity of the wave field. And it also contains the exact total energy of the true spectrum. Comparisons of this spectral model with the JONSWAP model and field data show excellent agreements. Thus we established an alternative approach for spectral models. Future research efforts should concentrate on relating the internal parameters to the external environmental variables.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 112 , November 1981 , pp. 203 - 224
Copyright
© 1981 Cambridge University Press

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References

Burling, R. W. 1959 The spectrum of wave at short fetches. Dtsch. Hydrogr. Z. 12, 45–64, 96–117.Google Scholar
Elliott, J. A. 1972 Microscale pressure fluctuations near waves being generated by the wind. J. Fluid Mech. 54, 427–448.Google Scholar
Hasselmann, K. 1962 On the non-linear energy transfer in a gravity wave spectrum. Part 1. J. Fluid Mech. 12, 481–500.Google Scholar
Hasselmann, K. 1963a On the non-linear energy transfer in a gravity wave spectrum. Part 2. J. Fluid Mech. 15, 273–81.Google Scholar
Hasselmann, K. 1963b On the non-linear energy transfer in a gravity wave spectrum. Part 3. J. Fluid Mech. 15, 385–398.Google Scholar
Hasselmann, K. 1973 Measurements of wind wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP). Herausgegeben von Deutsch. Hydrograph. Inst., Reihe A, no. 12.
Hasselmann, K., Ross, D. B., Müller, P. & Sell, W. 1976 A parametric wave prediction model. J. Physical Oceanog. 6, 200–228.Google Scholar
Hicks, B. L. 1960 The energy spectrum of small wind waves. Univ. Illinois, C.S.L. Rep. no-M-91.Google Scholar
Huang, N. E. & Long, S. R. 1980 An experimental study of the surface elevation probability distribution and statistics of wind generated waves. J. Fluid Mech. 101, 179–200.Google Scholar
Huang, N. E. & Tung, C. C. 1976 The dispersion relation for a nonlinear random gravity wave field. J. Fluid Mech. 75, 337–345.Google Scholar
Imasato, N. 1976 Some characteristics of the development process of the wind-wave spectrum. J. Oceanog. Soc. Japan 32, 27–32.Google Scholar
Kinsman, B. 1960 Surface waves at short fetches and low wind speed — A field study. Chesapeake Bay Inst. Johns Hopkins Univ. Tech. Rep. no. 19.Google Scholar
Kitaigorodskii, S. A. 1962 Applications of the theory of similarity to the analysis of wind-generated wave motion as a stochastic process. Izv. Geophys. Ser. Acad. Sci. U.S.S.R. 1, 105–117.Google Scholar
Liu, P. C. 1971 Normalized and equilibrium spectra of wind waves on Lake Michigan. J. Phys. Oceanog. 1, 249–257.Google Scholar
Longuet-Higgins, M. S. 1957 The statistical analysis of a random, moving surface. Phil. Trans. Roy. Soc. A 249, 321–387.Google Scholar
Longuet-Higgins, M. S. 1962 The statistical geometry of random surfaces. Hydrodynamic Stability: Proc. 13th Symp. Appl. Math., Providence, R.I., pp. 105–143. Amer. Math. Soc.
Longuet-Higgins, M. S. 1963 The effect of non-linearities on statistical distributions in the theory of sea waves. J. Fluid Mech. 17, 459–480.Google Scholar
Longuet-Higgins, M. S. 1980 On the distribution of the heights of sea waves: some effects of nonlinearity and finite band width. J. Geophys. Res. 85, 1519–1523.Google Scholar
Longuet-Higgins, M. S., Cartwright, D. E. & Smith, N. D. 1963 Observations of the directional spectrum of sea waves using the motions of a floating buoy. Ocean Wave Spectra, pp. 111–136. Prentice-Hall.
Mcgoogan, J. T. 1975 Satellite altimetry applications. I.E.E.E. Trans. MTT-23, pp. 970–978.
Mitsuyasu, H. 1968 On the growth of the spectrum of wind-generated waves (I.). Rep. Res. Inst. Appl. Mech., Kyushu Univ. 16 (55), 459–482.Google Scholar
Mitsuyasu, H., Tasi, F., Suhara, T., Mizuno, S., Ohkusu, M., Honda, T. & Rikiishi, K. 1980 Observation of the power spectrum of ocean waves using a cloverleaf buoy. J. Phys. Oceanog. 10, 286–296.Google Scholar
Müller, P. 1976 Parametrization of one-dimensional wind wave spectra and their dependence on the state of development. Hamburger geophysikalische Einzelschriften, Heft 31. Hamburg: G. M. L. Wittenborn Söhne.
Parsons, C. L. 1979 GEOS-3 wave height measurements: an assessment during high sea state conditions in the north Atlantic. J. Geophys. Res. 84, 4011–4020.Google Scholar
Phillips, O. M. 1958 The equilibrium range in the spectrum of wind generated waves. J. Fluid Mech. 4, 426–434.Google Scholar
Phillips, O. M. 1960 On the dynamics of unsteady gravity waves of finite amplitude. Part 1. J. Fluid Mech. 9, 193–217.Google Scholar
Phillips, O. M. 1961 On the dynamics of unsteady gravity waves of finite amplitude. Part 2. J. Fluid Mech. 11, 143–155.Google Scholar
Phillips, O. M. 1977 The Dynamics of the Upper Ocean. Cambridge University Press.
Pierson, W. J. 1962 The directional spectrum of a wind generated sea as determined from data obtained by the stereo wave observation project. Coll. Engng N.Y.U. Met. Paper 2, no. 6.
Pierson, W. J. & Moskowitz, L. 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.Google Scholar
Sutherland, A. J. 1968 Growth of spectral components in a wind-generated wave train. J. Fluid Mech. 33, 545–560.Google Scholar
Tick, L. J. 1959 A non-linear random model of gravity waves. Part 1. J. Math. Mech. 8, 643–652.Google Scholar
Toba, Y. 1973 Local balance in the air—sea boundary processes. III. On the spectrum of wind waves. J. Oceanog. Soc. Japan 29, 209–220.Google Scholar
Walsh, E. J. 1979 Extraction of ocean wave height and dominant wave length from GEOS-3 altimeter data. J. Geophys. Res. 84, 4003–4010.Google Scholar
Wu, J. 1975 Wind-induced drift currents. J. Fluid Mech. 68, 49–70.Google Scholar
Wu, H.-Y., Hsu, E. U. & Street, R. L. 1977 The energy transfer due to air input, non-linear wave—wave interaction, and whitecap dissipation associated with wind generated waves. Stanford Univ., Dept. Civil Engng Tech. Rep. 207.Google Scholar