Least Upper Bound Distribution for Nonlinear Wave Crests
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 128, Issue 4
Abstract
The exact form of the statistical distribution of nonlinear wave crests is not known. This study proposes and develops a theoretical least upper bound (lub) distribution for large crest heights within the framework of second-order deep-water wave theory. The form of the lub distribution is determined by a simple but specific parameterization of second-order nonlinearities so as to satisfy the theoretical upper-bound on the sea-surface skewness. The implications and various integral properties of the proposed distribution are then examined. Subsequently, these are compared with measurements gathered during Hurricane Camille and also with simulations of the same data recently carried out by Forristall. The comparisons clearly confirm the validity and utility of the proposed lub distribution for large wave crests in deep water.
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References
Al-Humoud, J., Tayfun, M. A., and Askar, H. (2002). “Distribution of nonlinear wave crests.” Ocean Eng., in press.
Askar, H., and Tayfun, M. A.(1999). “Exceedance distribution of large crest heights.” Kuwait J. Sci. Eng., 26, 225–238.
Cartwright, D. E., and Longuet-Higgins, M. S.(1956). “The statistical distribution of the maxima of a random function.” Proc., R. Soc. London, Ser. A, 237, 212–332.
Dawson, T. H., Kriebel, D. L., and Wallendorf, L. A.(1993). “Breaking waves in laboratory-generated JONSWAP seas.” Appl. Ocean. Res., 15, 85–93.
Forristall, G. Z.(2000). “Wave crest distributions: Observations and second-order theory.” J. Phys. Oceanogr., 30, 1931–1943.
Huang, N. E., Long, S. R., Tung, C. C., Yuen, Y., and Bliven, L. F.(1983). “A non-Gaussian statistical model for surface elevation of nonlinear random wave fields.” J. Geophys. Res., 88, 7597–7606.
Jha, A. K., and Winterstein, S. R. (2000). “Nonlinear random ocean waves: Prediction and comparison with data.” Proc. ETCE/OMAE 2000 Joint Conf., paper ETCE/OMAE 2000-6125, ASME, New York.
Kriebel, D. L., and Dawson, T. H.(1993a). “Distribution of crest amplitudes in severe seas with breaking.” J. Offshore Mech. Arct. Eng., 115, 9–15.
Kriebel, D. L., and Dawson, T. H. (1993b). “Nonlinearity in wave crest statistics.” Proc. 2nd Int. Conf. on Wave Measurement and Analysis, ASCE, New York, 61–75.
Longuet-Higgins, M. S.(1963). “The effect of nonlinearities on statistical distributions in the theory of sea waves.” J. Fluid Mech., 17, 459–480.
Longuet-Higgins, M. S. (1964). “Modified Gaussian distributions for slightly nonlinear variables.” Radio Sci. J. Res. NBS/USNC-URSI 68D(9), 1049–1062.
Longuet-Higgins, M. S.(1975). “On the joint distribution of the periods and amplitudes of sea waves.” J. Geophys. Res., 80(18), 2688–2694.
Phillips, O. M. (1977). The dynamics of the upper ocean, Cambridge University Press, London.
Prevosto, M., Krogstad, H. E., and Robin, A.(2000). “Probability distributions for maximum wave and crest heights.” Coastal Eng., 40, 329–360.
Tayfun, M. A.(1980). “Narrow-band nonlinear sea waves.” J. Geophys. Res., 85(C3), 1548–1552.
Tayfun, M. A.(1986a). “On narrow-band representation of ocean waves 1. Theory.” J. Geophys. Res., 91(C6), 7743–7752.
Tayfun, M. A.(1986b). “On narrow-band representation of ocean waves 2. Simulations.” J. Geophys. Res., 91(C6), 7753–7759.
Tayfun, M. A.(1990). “High-wave-number/frequency attenuation of wind-wave spectra.” J. Waterw., Port, Coastal Ocean Eng., 116(3), 381–398.
Tayfun, M. A.(1993). “Sampling-rate errors in statistics of wave heights and periods.” J. Waterw., Port, Coastal Ocean Eng., 119(2), 172–192.
Tayfun, M. A.(1994). “Distributions of envelope and phase in weakly nonlinear random waves.” J. Eng. Mech., 120(5), 1009–1025.
Tayfun, M. A., and Lo, J.-M.(1989). “Envelope, phase, and narrow-band models of sea waves.” J. Waterw., Port, Coastal Ocean Eng., 115(5), 594–613.
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Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 128 • Issue 4 • July 2002
Pages: 144 - 151
Copyright
Copyright © 2002 American Society of Civil Engineers.
History
Received: Jun 28, 2001
Accepted: Mar 8, 2002
Published online: Jun 14, 2002
Published in print: Jul 2002
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