Hostname: page-component-848d4c4894-v5vhk Total loading time: 0 Render date: 2024-06-21T05:55:55.526Z Has data issue: false hasContentIssue false
  • English
  • Français

Oblique instability of periodic waves in shallow water

Published online by Cambridge University Press:  12 April 2006

P. J. Bryant
P. J. Bryant
Affiliation:
Mathematics Department, University of Canterbury, Christchurch, New Zealand
Get access Rights & Permissions [Opens in a new window]

Abstract

Periodic permanent waves in shallow water are stable to periodic disturbances in the same direction, but are unstable to certain oblique periodic disturbances. A computer-assisted stability analysis is made of such waves for oblique disturbances with wavelengths comparable to and long compared with the fundamental wavelength. Regions of instability are calculated, and an explanation is given for the occurrence of instability. It is shown that disturbances in the same direction with a small margin of stability may cause a greater modification to the permanent wave in practice than do oblique unstable disturbances.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 86 , Issue 4 , 28 June 1978 , pp. 783 - 792
Copyright
© 1978 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 periodic wavetrains in nonlinear dispersive systems. Proc. Roy. Soc. A 299, 59–75.Google Scholar
Benney, D. J. & Roskes, G. J. 1969 Wave instabilities. Stud. Appl. Math. 48, 377–385.Google Scholar
Bryant, P. J. 1974 Stability of periodic waves in shallow water. J. Fluid Mech. 66, 81–96.Google Scholar
Davey, A. & Stewartson, K. 1974 On three-dimensional packets of surface waves. Proc. Roy. Soc. A 338, 101–110.Google Scholar
Hayes, W. D. 1973 Group velocity and nonlinear dispersive wave propagation. Proc. Roy. Soc. A 332, 199–221.Google Scholar
Phillips, O. M. 1974 Wave interactions. In Nonlinear Waves (ed. Leibovich S. & A. R. Seebass), pp. 186–211. Cornell University Press.
Whitham, G. B. 1974 Linear and Nonlinear Waves. Interscience.