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On the stability of Kelvin waves

Published online by Cambridge University Press:  26 April 2006

W. K. Melville ,
G. G. Tomasson  and
D. P. Renouard
W. K. Melville
Affiliation:
R. M. Parsons Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
G. G. Tomasson
Affiliation:
R. M. Parsons Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
D. P. Renouard
Affiliation:
Institut de Mecanique de Grenoble, Saint-Martin d'Heres, France
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Abstract

We consider the evolution of weakly nonlinear dispersive long waves in a rotating channel. The governing equations are derived and approximate solutions obtained for the initial data corresponding to a Kelvin wave. In consequence of the small nonlinear speed correction it is shown that weakly nonlinear Kelvin waves are unstable to a direct nonlinear resonance with the linear Poincaré modes of the channel. Numerical solutions of the governing equations are computed and found to give good agreement with the approximate analytical solutions. It is shown that the curvature of the wavefront and the decay of the leading wave amplitude along the channel are attributable to the Poincaré waves generated by the resonance. These results appear to give a qualitative explanation of the experimental results of Maxworthy (1983), and Renouard, Chabert d'Hières & Zhang (1987).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 206 , September 1989 , pp. 1 - 23
Copyright
© 1989 Cambridge University Press

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