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The stability of steep gravity waves. Part 2

Published online by Cambridge University Press:  20 April 2006

Mitsuhiro Tanaka
Mitsuhiro Tanaka
Affiliation:
Department of Applied Mathematics, Faculty of Engineering, Gifu University, 1-1 Yanagido, Gifu, 501 - 11 Japan
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Abstract

In the previous work (Tanaka 1983), the linear stability problem of surface gravity waves on deep water to ‘superharmonic’ disturbances was investigated. The result obtained there suggested that the waves lose stability at the steepness which corresponds to the maximum total energy and the impulse. This result, however, apparently contradicts other work and thus the validity of it has been regarded as questionable. In the present paper, the validity of our previous result is first confirmed by two independent methods. Then, it is also shown that the contradictions with other works will disappear in a natural way when the explicit form of the unstable disturbance around the critical steepness is appropriately taken into account.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 156 , July 1985 , pp. 281 - 289
Copyright
© 1985 Cambridge University Press

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References

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