Hostname: page-component-cb9f654ff-lqqdg Total loading time: 0 Render date: 2025-08-31T07:30:11.733Z Has data issue: false hasContentIssue false
  • English
  • Français

Instabilities of finite-amplitude water waves

Published online by Cambridge University Press:  20 April 2006

John W. McLean
John W. McLean
Affiliation:
Fluid Mechanics Department, TRW Defense and Space Systems Group, Redondo Beach, California, CA 90278
Get access Rights & Permissions [Opens in a new window]

Abstract

A numerical investigation of normal-mode perturbations of a finite-amplitude Stokes wave has revealed regions of instability lying near resonance curves given by the linear-dispersion relation. It is found that, for small amplitude, the dominant instability is two-dimensional (of Benjamin-Fier type) but, for larger amplitudes, the dominant instability becomes a three-dimensional perturbation. Results are compared with recent experimental observations of steep wave trains.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 114 , January 1982 , pp. 315 - 330
Copyright
© 1972 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.)

Article purchase

Temporarily unavailable

References

Benjamin, T. B. & Feir, J. E. 1967 The disintegration of wavetrains on deep water. J. Fluid Mech. 27, 417–430.Google Scholar
Chen, B. & Saffman, P. G. 1980 Numerical evidence for the existence of new types of gravity waves of permanent form on deep water. Stud. Appl. Math. 62, 1–21.Google Scholar
Cokelet, E. D. 1977 Steep gravity waves in water of uniform arbitrary depth. Phil. Trans. R. Soc. Lond. A 286, 184–230.Google Scholar
Crawford, D. R., Lake, B. M., Saffmann, P. G. & Yuen, H. C. 1981 Stability of weakly nonlinear deep-water waves in two and three dimensions. J. Fluid Mech. 105, 177–192.Google Scholar
Dagan, G. 1975 Taylor instability of a non-uniform free-surface flow. J. Fluid Mech. 67, 113–123.Google Scholar
Hasselmann, D. E. 1979 The high wavenumber instabilities of a Stokes wave. J. Fluid Mech. 93, 491–500.Google Scholar
Lighthill, M. J. 1965 Contributions to the theory of waves in nonlinear dispersive systems. J. Inst. Math. Appl. 1, 269–306.Google Scholar
Longuet-Higgins, M. S. 1978a 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. 1978b Some new relations between Stokes coefficients in the theory of gravity waves. J. Inst. Math. Applic. 22, 261–273.Google Scholar
Mclean, J. W., Ma, Y. C., Martin, D. U., Saffman, P. G. & Yuen, H. C. 1981 Three-dimensional instability of finite amplitude water waves. Phys. Rev. Lett. 46, 817–820.Google Scholar
Phillips, O. M. 1960 On the dynamics of unsteady gravity waves of finite amplitude. J. Fluid Mech. 9, 193–217.Google Scholar
Phillips, O. M. 1981 The dispersion of short wavelets in the presence of a dominant long wave. Unpublished manuscript.
Saffman, P. G. 1980 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 wave of permanent form. J. Fluid Mech. 101, 797–808.Google Scholar
Schwartz, L. W. 1974 Computer extension and an analytic continuation of Stokes expansion for gravity waves. J. Fluid Mech. 62, 553–578.Google Scholar
Su, M. Y. 1981 Three-dimensional deep-water waves. Part I. Laboratory experiments on spilling breakers. Unpublished manuscript.
Zakharov, Y. 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