Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-19T02:53:38.515Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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