Non‐Gaussian Properties of Second‐Order Random Waves
Publication: Journal of Engineering Mechanics
Volume 119, Issue 2
Abstract
Under the assumption that the second‐order random wave theory is valid, theoretical solutions for the probabilistic cumulants (or moments), in particular the third and fourth cumulants, of wave elevation associated with a deep‐water unidirectional random wave of arbitrary wave bandwidth are derived. In general, knowing the probability density function is not sufficient to obtain the corresponding power spectral density function, and vice versa. However, through the use of the second‐order random wave theory, the study shows that the probabilistic cumulants and spectral parameters of stationary random wave processes become closely related. In the present paper, numerical attention is given to random waves described by either Pierson‐Moskowitz, JONSWAP, or Wallops spectra. The paper also numerically verifies that the use of the second‐order random wave theory is appropriate only when the significant wave slope is less than about 0.02.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Borgman, L. E. (1969). “Ocean wave simulation for engineering design.” J. Wtrwy. and Harb. Div., ASCE, 95(4), 557–581.
2.
Chakrabarti, S. K. (1987). HydrOdynamics of offshore structures. Computational Mechanics Publications, New York, N.Y.
3.
Earle, M. D. (1975). “Extreme wave conditions during Hurricane Camile.” J. Geophysical Res., 80, 377–379.
4.
Forristall, G. Z. (1978). “On the statistical distribution of wave heights in a storm.” J. Geophysical Res., 83, 2353–2358.
5.
Hasselmann, K. (1962). “On the nonlinear energy transfer in a gravity‐wave spectrum, part 1, general.” J. Fluid Mech., 12, 481–500.
6.
Hasselmann, K. (1963). “On the nonlinear energy transfer in a gravity‐wave spectrum, part 2, conservation theorems, wave particle correspondence, irreversibility.” J. Fluid Mech., 15, 273–281.
7.
Hu, S.‐L. J. (1991). “Probabilistic independence and joint cumulants.” J. Engrg. Mech., ASCE, 117(3), 640–652.
8.
Huang, N. E., and Long, S. R. (1980). “An experimental study of the surface elevation probability distribution and statistics of wind generated wave.” J. Fluid Mech., 101, 179–200.
9.
Huang, N. E., Long, S. R., Tung, C. C., Yuen, Y., and Bliven, L. F. (1981). “A unified two‐parameter wave spectral model for a general sea state.” J. Fluid Mech., 112, 203–224.
10.
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 field.” J. Geophys. Res., 88, 7597–7606.
11.
Huang, N. E., Tung, C. C., and Long, S. R. (1990). “Wave spectra.” The Sea, B LeMahante, ed., Vol. 9, John Wiley and Sons, Inc., New York, N.Y., 197–238.
12.
Hudspeth, R. T., and Chen, M. C. (1979). “Digital simulation of nonlinear random waves.” J. Wtrwy., Port, Coast. and Oc. Div., ASCE, 105(1), 67–85.
13.
Longuet‐Higgins, M. S. (1963). “The effect of non‐linearities on statistical distributions in the theory of sea waves.” J. Fluid Mech., 17(3), 459–480.
14.
Madsen, H. O., Krenk, S., and Lind, N. C. (1986). Methods of structural safety. Prentice‐Hall, Inc., Englewood Cliffs, N.J.
15.
Sarpkaya, T., and Isaacson, M. (1981). Mechanics of wave forces on offshore structures. Van Nostrand Reinhold Co., Inc., New YoRk, N.Y.
16.
Sharma, J. N., and Dean, R. G. (1979). “Development and evaluation of a procedure for simulating a random directional second order sea surface and associated wave forces.” Ocean Engrg. Report 20, University of Delaware, Newark, Del.
17.
Tayfun, M. A. (1986). “On narrow‐band representation of ocean waves.” J. Geophys. Res., 91(6), 7743–7752.
18.
Tick, L. J. (1959). “A nonlinear random model of gravity waves I.” J. Mathematics and Mech., 8, 643–651.
Information & Authors
Information
Published In
Copyright
Copyright © 1993 American Society of Civil Engineers.
History
Received: Apr 29, 1991
Published online: Feb 1, 1993
Published in print: Feb 1993
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.