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Long-time evolution of an unstable water-wave train

Published online by Cambridge University Press:  20 April 2006

Michael Stiassnie  and
Uri I. Kroszynski
Michael Stiassnie
Affiliation:
Department of Civil Engineering and Coastal & Marine Engineering Research Institute, Technion, I.I.T., Technion City, Haifa 32000, Israel
Uri I. Kroszynski
Affiliation:
Department of Civil Engineering and Coastal & Marine Engineering Research Institute, Technion, I.I.T., Technion City, Haifa 32000, Israel
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Abstract

The long-time evolution of an unstable wave train, consisting of a carrier wave and two 'side-band’ components, is investigated analytically. Mathematical expressions, involving Jacobian elliptic functions, for the wave envelope characteristics are derived. The solution yields the dependence of the long-time evolution on the initial disturbance. Of special interest is the simple formula for the modulation-demodulation recurrence period. The latter is shown to yield results in good agreement with those obtained from numerical solutions of the nonlinear Schrödinger equation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 116 , March 1982 , pp. 207 - 225
Copyright
© 1982 Cambridge University Press

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