Hostname: page-component-7479d7b7d-qlrfm Total loading time: 0 Render date: 2024-07-10T09:31:36.535Z Has data issue: false hasContentIssue false
  • English
  • Français

A criterion for nonlinear wave stability

Published online by Cambridge University Press:  28 March 2006

K. Hasselmann
K. Hasselmann
Affiliation:
University of Hamburg
Get access Rights & Permissions [Opens in a new window]

Abstract

Nonlinear resonant wave triads composed of one finite and two infinitesimal components are unstable for sum interactions and neutrally stable for difference interactions. A similar criterion holds for tertiary interactions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 30 , Issue 4 , 22 December 1967 , pp. 737 - 739
Copyright
© 1967 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. 1967 Instability of period wave trains in nonlinear dispersive systems. Proc. Roy. Soc. A 299, 59–75.Google Scholar
Benjamin, T. B. & Feir, J. E. 1967 The disintegration of wave trains on deep water. Part 1. Theory. J. Fluid Mech. 27, 417–30. Part 2. Experiments. J. Fluid Mech. (to appear).Google Scholar
Davis, R. E. & Acrivos, A. 1967 The stability of oscillatory internal waves. J. Fluid Mech. 30, 723.Google Scholar
Hasselmann, K. 1966 Feynman diagrams and interaction rules of wave—wave scattering processes. Rev. Geophys. 4, 1–32.Google Scholar
Kelly, R. E. 1965 The stability of an unsteady Kelvin—Helmholtz flow. J. Fluid Mech. 22, 547–60.Google Scholar
Kelly, R. E. 1967 On the stability of an inviscid shear layer which is periodic in space and time. J. Fluid Mech. 27, 657–89.Google Scholar
Longuet-Higgins, M. S. & Phillips, O. M. 1962 Phase velocity effects in tertiary wave interactions. J. Fluid Mech. 12, 333–336.Google Scholar
Whitham, G. B. 1966 Nonlinear dispersion of water waves. J. Fluid Mech. 27, 399–412.Google Scholar
Whitham, G. B. 1967 Variational methods and applications to water waves. Proc. Roy. Soc. A 299, 6–25.Google Scholar