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On the stability of gravity waves on deep water

Published online by Cambridge University Press:  26 April 2006

Christian Kharif  and
Alfred Ramamonjiarisoa
Christian Kharif
Affiliation:
Institut de Mécanique Statistique de la Turbulence, 12 Avenue General Lederc, 13003 Marseille, France
Alfred Ramamonjiarisoa
Affiliation:
Institut de Mécanique Statistique de la Turbulence, 12 Avenue General Lederc, 13003 Marseille, France
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Abstract

This note presents numerical results on the stability of large-amplitude gravity waves on deep water. The results are then used to predict new two-dimensional superharmonic instabilities. They are due to collisions of eigenvalues of opposite signatures, confirming the recent condition for instability of MacKay & Saffman (1986).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 218 , September 1990 , pp. 163 - 170
Copyright
© 1990 Cambridge University Press

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References

Benjamin, T. B. & Feir, J. E., 1967 The disintegration of wave trains on deep water. J. Fluid Mech. 27, 417–430.Google Scholar
Branger, H., Ramamonjiarisoa, A. & Kharif, C., 1986 Sur la stabilité des vagues de gravité de fortes cambrures aux perturbations sous harmoniques. J. Mec. Theor. Appl. 5, 535–550.Google Scholar
Dysthe, K. B.: 1979 Note on a modification to the non linear Schrödinger equation for application to deep water waves. Proc. R. Soc. Lond. A 369, 105–114.Google Scholar
Feir, J. E.: 1967 Discussion: some results from wave pulse experiments. Proc. R. Soc. Lond. A 299, 54.Google Scholar
Hogan, S. J.: 1988 The superharmonic normal mode instabilities of nonlinear deep-water capillary waves. J. Fluid Mech. 190, 165–177.Google Scholar
Kharif, C.: 1987 Etude comparative des instabilités tridimensionnelles et bidimensionnelles des vagues de gravité de fortes cambrures. J. Mec. Theo. Appl. 6, 843–864.Google Scholar
Kharif, C.: 1990 Some aspects of the kinematics of short waves over long waves. In Water Wave kinematics Advanced Research Workshop (ed. A. Tørum & O. T. Gudmestad). Kluwer.
Kharif, C. & Ramamonjiarisoa, A., 1988 Deep water gravity wave instabilities at large steepness. Phys. Fluids 31, 1286–1288.Google Scholar
Lake, B. M., Yuen, H. C., Rungaldier, H. & Ferguson, W. E., 1977 Nonlinear deep-water waves: theory and experiments. Part 2. Evolution of a continuous wave train. J. Fluid Mech. 83, 49–74.Google Scholar
Longuet-Higgins, M. S.: 1978a The instabilities of gravity waves of finite amplitude in deep-water. I. Super harmonics. Proc. R. Soc. Lond. A 360, 471–488.Google Scholar
Longuet-Higgins, M. S.: 1978b The instabilities of gravity waves of finite amplitude in deep-water. II. Subharmonics. Proc. R. Soc. Lond. A 360, 489–505.Google Scholar
Longuet-Higgins, M. S.: 1985 Bifurcation in gravity waves. J. Fluid Mech. 151, 457–475.Google Scholar
Longuet-Higgins, M. S.: 1986 Bifurcation and instability in gravity waves. Proc. R. Soc. Lond. A 403, 167–187.Google Scholar
MacKay, R. S. & Saffman, P. G., 1986 Stability of water waves. Proc. R. Soc. Lond. A A406, 115–125.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. V., Saffman, P. G. & Yuen, H. C., 1981 Three-dimensional instability of finite amplitude water waves. Phys. Rev. Lett. 46, 817–820.Google Scholar
Stiassnie, M. & Shemer, L., 1984 On modifications of the Zakharov equation for surface gravity waves. J. Fluid Mech. 143, 47–67.Google Scholar
Su, M. Y.: 1982 Three-dimensional deep-water waves. Part 1. Experimental measurement of skew and symmetric wave patterns. J. Fluid Mech. 124, 73–108.Google Scholar
Tanaka, M.: 1983 The stability of steep gravity waves. J. Phys. Soc. Japan 52, 3047–3055.Google Scholar
Tanaka, M.: 1985 The stability of steep gravity waves. Part 2. J. Fluid Mech. 156, 281–289.Google Scholar
Voronovich, A. G., Lobanov, E. D. & Rybak, S. A., 1980 On the stability of gravitational–capillary waves in the presence of a vertically nonuniform current. Izv. Atm. Ocean Phys., 16, 220–222.Google Scholar
Witham, G. B.: 1974 Linear and Nonlinear Waves. Wiley.
Zakharov, V. E.: 1968 Stability of period waves of finite amplitude on the surface of a deep fluid. Z. Angew. Math. Phys. 9, 86–94.Google Scholar
Zhang, J. & Melville, W. K., 1987 Three-dimensional instabilities of nonlinear gravity–capillary waves. J. Fluid Mech. 174, 187–208.Google Scholar