TECHNICAL PAPERS
Mar 1, 1997

Numerically Simulating Non-Gaussian Sea Surfaces

Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 123, Issue 2

Abstract

A technique to simulate non-Gaussian time series with a desired (“target”) power spectrum and bispectrum is applied to ocean waves. The targets were obtained from observed bottom pressure fluctuations of shoaling, nonbreaking waves in 2–9 m water depth. The variance (i.e., frequency integrated spectrum), skewness, and asymmetry (i.e., frequency integrated bispectrum) of the simulated time series compare favorably with the observations, even for highly skewed and asymmetric near-breaking waves. The mean lengths of groups of high waves from non-Gaussian simulated time series are closer to observed values than those from Gaussian simulations. The simulations suggest that quadratic phase coupling between waves (of different frequencies) in shallow water results in longer wave groups than occur with linear, uncoupled waves having the identical power spectrum.

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References

1.
Andrew, M. E., and Borgman, L. E. (1981). “Procedures for studying wave grouping in wave records from California Coastal Data Collection Program.”Rep., U.S. Army Corps of Engrs., San Francisco, Calif., Nov.
2.
Battjes, J. A., and van Vledder, G. P. (1994). “Verification of Kimura's theory for wave group statistics.”Proc., 19th Int. Coast. Engrg. Conf., ASCE, New York, N.Y., 642–648.
3.
Elgar, S., and Chandran, V.(1993). “Higher-order spectral analysis to detect nonlinear interactions in measured time series and an application to Chua's circuit.”Int. J. Bifurcation and Chaos, 3, 19–34.
4.
Elgar, S., and Guza, R. T.(1985a). “Shoaling gravity waves: comparisons between field observations, linear theory, and a nonlinear model.”J. Fluid Mech., 158, 47–70.
5.
Elgar, S., and Guza, R. T.(1985b). “Observations of bispectra of shoaling surface gravity waves.”J. Fluid Mech., 161, 425–448.
6.
Elgar, S., Guza, R. T., Raubenheimer, B., Herbers, T. H. C., and Gallagher, E. (1997). “Spectral evolution of shoaling and breaking waves on a barred beach.” submitted to J. Geophys. Res.
7.
Elgar, S., Guza, R. T., and Seymour, R.(1984). “Groups of waves in shallow water.”J. Geophys. Res., 89, 3623–3634.
8.
Elgar, S., Guza, R. T., and Seymour, R. (1985). “Wave group statistics from numerical simulations of a random sea.”Appl. Oc. Res., 7, 212–237.
9.
Gill, P. E., and Murray, W.(1978). “Algorithms for the solution of the nonlinear least-squares problem.”SIAM J. Numer. Anal., 15, 977–992.
10.
Goda, Y. (1983). “Analysis of wave grouping and spectra of long-traveled swell.”Rep. 22, Port and Harb. Res. Inst., Nagase, Yokosuka, Japan, 3–41.
11.
Haubrich, R. A.(1984). “Earth noise, 5 to 500 millicycles per second.”J. Geophys. Res., 70, 1415–1427.
12.
Hasselmann, K., Munk, W., and MacDonald, G. (1963). “Bispectra of ocean waves.”Time Series Analysis, M. Rosenblatt, ed., Wiley, New York, N.Y., 125–139.
13.
Jenkins, G., and Watts, D. (1968). Spectral analysis and its applications. Holden-Day, San Francisco, Calif.
14.
Kim, Y. C., and Powers, E. J.(1979). “Digital bispectral analysis and its applications to nonlinear wave interactions.”IEEE Trans. on Plasma Sci., 7, 120–131.
15.
Liu, Z., Elgar, S., and Guza, R. T.(1993). “Groups of ocean waves: Comparisons between linear theory, approximations to linear theory, and observations.”J. Wtrwy., Port, Coast., and Oc. Engrg., ASCE, 119(2), 144–159.
16.
Longuet-Higgins, M. S.(1952). “On the statistical distribution of the heights of sea waves.”J. Marine Res., 9, 245–266.
17.
Longuet-Higgins, M. S.(1975). “On the joint distribution of the periods and amplitudes of sea waves.”J. Geophys. Res., 80, 2688–2694.
18.
Longuet-Higgins, M. S.(1984). “Statistical properties of wave groups in a random sea state.”Philosophical Trans. Royal Soc., London, U.K., Ser. A, 312, 219–250.
19.
Medina, J. R., and Hudspeth, R. T.(1990). “A review of the analysis of ocean wave groups.”Coast. Engrg., 14, 515–542.
20.
Nikias, C. L., and Raghuveer, M. R.(1987). “Bispectral estimation: A digital signal processing approach.”Proc., IEEE, 75, 869–891.
21.
Rice, S. O. (1954). “Mathematical analysis of random noise.”Selected papers on noise and stochastic processes, N. Wax, ed., Dover Publications, Inc., New York, N.Y.
22.
Schetzen, M. (1980). The Volterra and Wiener theories of nonlinear systems. Wiley, New York, N.Y.
23.
Thomas, K., Baba, M., and Harish, C.(1986). “Wave groupiness in long-traveled swell.”J. Wtrwy., Port, Coast., and Oc. Engrg., ASCE, 112(4), 498–511.
24.
Vanhoff, B., and Elgar, S. (1997). “Simulating quadratically nonlinear random processes.”Int. J. Bifurcation and Chaos, in press.

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Published In

Go to Journal of Waterway, Port, Coastal, and Ocean Engineering
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 123Issue 2March 1997
Pages: 68 - 72

History

Published online: Mar 1, 1997
Published in print: Mar 1997

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Authors

Affiliations

Barry Vanhoff
Res. Assoc., School of Electrical Engrg. and Comp. Sci., Washington State Univ., Pullman, WA 99164-2752.
Steve Elgar
Prof., School of Electrical Engrg. and Comp. Sci., Washington State Univ., Pullman, WA.
R. T. Guza
Prof., Ctr. for Coast. Studies, Univ. of California, 9500 Gilman Dr., La Jolla, CA 92093-0209.

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