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Three-dimensional deep-water waves. Part 1. Experimental measurement of skew and symmetric wave patterns

Published online by Cambridge University Press:  20 April 2006

Ming-Yang Su
Ming-Yang Su
Affiliation:
Naval Ocean Research and Development Activity, NSTL Station, Mississippi 39529
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Abstract

The three-dimensional structures of symmetric and skew wave patterns in deep water observed in a tow tank and a wide basin are described. These symmetric waves are the result of three-dimensional subharmonic bifurcation of two-dimensional wave-trains with steepness a0k0 ≥ 0·25, where a0, and k0, are the wave amplitude and wave-number respectively. The wave profiles, local surface slopes and amplitude spectra at various cross-sections of the crescent-shaped symmetric waves are presented and discussed.

The skew waves are another type of three-dimensional bifurcation from a uniform wavetrain, and occur most clearly when 0·16 [siml ] a0k0 [siml ] 0·18. These skew wave patterns are found to interact between two sets of themselves propagating from different directions, and to be subject to the Benjamin–Feir type modulations. The interactions cause compact three-dimensional wave packets. Agreement between experiment and theory is found for the case of symmetric wave patterns. The bifurcation of uniform Stokes waves into symmetric wave patterns provide a new physical process for directional energy spreading.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 124 , November 1982 , pp. 73 - 108
Copyright
© 1982 Cambridge University Press

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References

Benjamin, T. B. & Feir, J. E. 1967 The disintegration of wave trains on deep water. Part 1. Theory. J. Fluid Mech. 27, 417–430.Google Scholar
Cokelet, E. D. 1977 Breaking waves. Nature 267, 769–774.Google Scholar
Crawford, P. R., Lake, B. M., Saffman, P. G. & Yuen, H. C. 1981 Stability of weakly non-linear deep-water waves in two and three dimensions. J. Fluid Mech. 105, 177–191.Google Scholar
Donelan, M., Longuet-Higgins, M. S. & Turner, J. S. 1972 Periodicity in white caps. Nature 239, 449–450.Google Scholar
Gross, M. G. 1977 Oceanography — A View of the Earth. Prentice-Hall.
Hui, W. H. & Hamilton, J. 1979 Exact solutions of a three-dimensional nonlinear Schrödinger equation applied to gravity waves. J. Fluid Mech. 93, 117–133.Google Scholar
King, P. G. & Shemdin, O. H. 1978 Radar observations of hurricane wave directions. In Proc. 16th Coast Engng Conf..
Kinsman, B. 1965 Wind Waves. Prentice-Hall.
Longuet-Higgins, M. S. 1976 On the nonlinear transfer of energy in the peak of a gravity-wave spectrum: a simplified model. Proc. R. Soc. Lond. A 347, 331–328.Google Scholar
Longuet-Higgins, M. S. 1978 The instabilities of gravity waves of finite amplitude in deep water. II. Subharmonics. Proc. R. Soc. Lond. A 360, 489–505.Google Scholar
Mclean, J. W. 1982 Instabilities of finite-amplitude water waves. J. Fluid Mech. 114, 315–330.Google Scholar
Mclean, J. W., Ma, Y. C., Martin, D. U., Saffman, P. G. & Yuen, H. C. 1981 A new type of three-dimensional instability of finite-amplitude waves. Phys. Rev. Lett. 46, 817–820.Google Scholar
Meiron, D. I., Saffman, P. G. & Yuen, H. C. 1982 Calculation of steady three-dimensional deep-water waves. J. Fluid Mech. 124, 109–121.Google Scholar
Peregrine, D. H. & Thomas, G. P. 1979 Finite amplitude deep water wave on currents. Phil. Trans. R. Soc. Lond. A 292, 371–390.Google Scholar
Saffman, P. G. 1981 Long wavelength bifurcation of gravity waves on deep water. J. Fluid Mech. 101, 567–581.Google Scholar
Saffman, P. G. & Yuen, H. C. 1980 A new type of three-dimensional deep-water waves of permanent form. J. Fluid Mech. 101, 797–808.Google Scholar
Su, M.-Y. 1981 Long-time evolution of deep-water surface wave trains of moderate steepness (unpublished manuscript).
Su, M.-Y., Bergin, M., Marler, P. & Myrick, R. 1982 Experiments on nonlinear instabilities and evolution of steep gravity-wave trains. J. Fluid Mech. 124, 45–72.Google Scholar
Zakharov, V. E. 1968 Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys. 2, 190–194.Google Scholar