High‐Wave‐Number/Frequency Attenuation of Wind‐Wave Spectra
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 116, Issue 3
Abstract
Properties of surface‐elevation spectra representative of nonlinear deep‐water wind waves are examined theoretically. For a wave field characterized by second‐order nonlinearities, expressions describing the spatial covariance and the directional wave‐number spectrum of the surface geometry are derived. The nature of these quantities are then examined with emphasis on the high‐wave‐number attenuation of spectral amplitudes. It is found that, if the spectrum of the firstorder linear wave field decays as toward the high‐wave‐number extreme, then the spectrum of the nonlinear wave field must decay as This condition coupled with the saturation/equilibrium range concepts is shown to necessitate the existence of certain upper‐limit asymptotes to the high‐frequency attenuation of linear‐wave spectra. Practical implications of this result are explored with reference to low‐pass filtering of wave records, and the representation of Gaussian sea waves based on various empirical and/or theoretical forms of wind‐wave spectra.
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References
1.
Barrick, D. E., and Weber, B. L. (1977). “On the nonlinear theory for gravity waves on the ocean's surface: 2. Interpretation and applications.” J. Physical Oceanography, 7(1), 11–21.
2.
Forristall, G. Z. (1981). “Measurements of a saturated range in ocean wave spectra.” J. Geophysical Res., 86 (C9), 8075–8084.
3.
Fox, M. J. H. (1976). “On the nonlinear transfer of energy in the peak of a gravity‐wave spectrum II.” Proc., Royal Soc. of London, London, England, 348, 467–483.
4.
Glazman, R. E., (1986). “Statistical characterization of sea surface geometry for a wave slope field discontinuous in the mean square.” J. Geophysical Res., 91 (C5), 6629–6641.
5.
Hasselmann, K. (1962). “On the nonlinear energy transfer in a gravity‐wave spectrum: 1. General theory.” J. Fluid Mech., 12, 481–500.
6.
Hasseman, K., et al. (1973). “Measurements of wind wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP).” Deutschen Hydrographischen Zeitschrift, Hamburg, Germany, Supplement A, 8 (12), 1–95.
7.
Hildebrand, F. B. (1976). Advanced calculus for applications, 2nd Ed., Prentice‐Hall, Inc., Englewood Cliffs, N.J., 264.
8.
Huang, N. E., et al. (1981). “A unified two‐parameter wave spectral model for a general sea state.” J. Fluid Mech., 112, 203–224.
9.
Kitaigorodski, S. A. (1962). “Applications of the theory of similarity to the analysis of wind‐generated wave motions as a stochastic process.” Bulletin Acad. Sci. USSR, Geophysical Series, 73–80.
10.
Kitaigorodski, S. A., (1983). “On the theory of the equilibrium range in the spectrum of wind‐generated gravity waves.” J. Physical Oceanography, 13(May),810–827.
11.
Longuet‐Higgins, M. S. (1963). “The effect of nonlinearities on statistical distributions in the theory of sea waves.” J. Fluid Mech., 17, 459–480.
12.
Longuet‐Higgins, M. S. (1976). “On the nonlinear transfer of energy in the peak of a gravity‐wave spectrum: A simplified model.” Proc., Royal Soc. London, London, England, 347, 311–328.
13.
Longuet‐Higgins, M. S. (1984). “Statistical properties of wave groups in a random sea state.” Philosophical Transactions, Royal Society of London, 312, 219–250.
14.
Nath, J. H., and Yeh, R. C. (1987). “Some time and frequency relations in random waves.” J. Waterway, Port, Coastal and Ocean Engrg., ASCE, 113(6), 672–683.
15.
Nolte, K. G., and Hsu, F. H. (1979). “Statistics of larger waves in a sea state.” J. Waterway, Port, Coastal and Ocean Div., ASCE, 105(4), 389–404.
16.
Phillips, O. M. (1958). “The equilibrium range in the spectrum of wind‐generated ocean waves.” J. Fluid Mech., 4, 426–434.
17.
Phillips, O. M. (1977). The dynamics of the upper ocean. Cambridge University Press, London, England.
18.
Phillips, O. M. (1985). “Spectral and statistical properties of the equilibrium range in wind‐generated gravity waves.” J. Fluid Mech., 156, 505–531.
19.
Tayfun, M. A., (1986). “On narrow‐band representation of ocean waves: 1. Theory.” J. Geophysical Res., 91 (C6), 7743–7752.
20.
Tayfun, M. A., and Lo, J.‐M. (1989). “Envelope, phase, and narrow‐band models of sea waves.” J. Waterway, Port, Coastal and Ocean Engrg., ASCE, 115(5), 594–613.
21.
Tayfun, M. A., and Lo, J.‐M. (1990). “Nonlinear effects on wave envelope and phase.” J. Waterway, Port, Coastal, and Ocean Engrg., ASCE, 116(1), 79–100.
22.
Tick, L. J. (1959). “A nonlinear random model of gravity wave I.” J. Mathematics Mech., 8, 643–652.
23.
Weber, B. L., and Barrick, D. E. (1977). “On the nonlinear theory for gravity waves on the ocean's surface: 1. Derivations.” J. Physical Oceanography, 7(1), 3–10.
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Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 116 • Issue 3 • May 1990
Pages: 381 - 398
Copyright
Copyright © 1990 ASCE.
History
Published online: May 1, 1990
Published in print: May 1990
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