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Nonlinear model predictions of bispectra of shoaling surface gravity waves

Published online by Cambridge University Press:  21 April 2006

Steve Elgar  and
R. T. Guza
Steve Elgar
Affiliation:
College of Engineering, University of Idaho, Moscow, ID 83 843, USA
R. T. Guza
Affiliation:
Scripps Institution of Oceanography, University of California, La Jolla, CA 92093, USA
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Abstract

Boussinesq-type nonlinear equations for waves propagating over a sloping bottom are shown to accurately model the evolving bispectra of a spectrum of non-breaking shoaling ocean-surface gravity waves. The model response to a variation of the gentle, constant beach slope and the amount of nonlinear (i.e. non-random) phase coupling in the initial conditions is also examined. Variation of these quantities results in relatively little change in the overall structural evolution of the bicoherence and biphase (related to the nonlinear modification of the wave shape). The apparent unimportance of bottom slope motivates consideration of constant-depth KdV equations. Simple analytic solutions are found for harmonic growth in the special case of a monochromatic primary wavetrain. The associated bispectral evolution is qualitatively similar to field observations and to predictions based on the full Boussinesq model for a sloping bottom.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 167 , June 1986 , pp. 1 - 18
Copyright
© 1986 Cambridge University Press

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References

Bkyant, P. J. 1973Periodic waves in shallow water. J. Fluid Mech. 59, 625–644.
Elgar, S. & Guza, R. T. 1985a Shoaling gravity waves: comparisons between field observations, linear theory, and a nonlinear model. J. Fluid Mech. 158, 47–70.Google Scholar
Elgar, S. & Guza, R. T. 1985b Observations of bispectra of shoaling surface gravity waves. J.Fluid Mech. 161, 425–448.Google Scholar
Flick, R. E., Guza, R. T. & Inman, D. L. 1981 Elevation and velocity measurements of laboratory shoaling waves. J. Geophys. Res. 86, 4149–4160.Google Scholar
Freilich, M. H. & Guza, R. T. 1984 Nonlinear effects on shoaling surface gravity waves. Phil.Trans. R. Soc. Lond. A 31, 1–41.Google Scholar
Hasselman, K., Munk, W. & Macdonald, G. 1963 Bispectra of ocean waves. In Time, Series Analysis (ed. M. Rosenblatt), pp. 125–139. Wiley.
Haubrich, R. A. 1965 Earth noises, 5 to 500 millicycles per second, 1. J. Geophys. Res. 70, 1415–1427.Google Scholar
Kim, Y. C. & Powers, E. J. 1979 Digital bispectral analysis and its application to nonlinear wave interactions. IEEE Trans, on Plasma Science, 1, 120–131.Google Scholar
Kim, Y. C., Beall, J. M., Powers, E. J. & Miksad, R. W. 1980 Bispectrum and nonlinear wave coupling. Phys. Fluids 23, 250–263.Google Scholar
Mei, C. C. & Uunlüata, U. 1972 Harmonic generation in shallow water waves. In Waves on Beaches and Resulting Sediment Transport (ed. R. Meyer), pp. 181–202. Academic.
Peregrine, D. H. 1967 Long waves on a beach. J. Fluid Mech. 27, 815–827.Google Scholar
Svendsen, I. A. & Buhr-Hansen, J. 1978 On the deformation of periodic long waves over a gently sloping bottom. J. Fluid Mech. 87, 433–448.Google Scholar