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Local stability of Gerstner's waves

Published online by Cambridge University Press:  28 April 2004

STÉPHANE LEBLANC
STÉPHANE LEBLANC
Affiliation:
Laboratoire de Sondages Electromagnétiques de l'Environnement Terrestre Université du Sud Toulon-Var, BP 20132, 83957 La Garde cedex, France
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Abstract

A general method is presented to investigate the hydrodynamic stability of ideal incompressible or barotropic flows described in a Lagrangian representation. Based on the theory of short-wavelength instabilities, the problem is reduced to a transport equation which involves only the distortion matrix of the equilibrium flow. The theory is applied to Gerstner's rotational free-surface gravity waves. It is shown that they are three-dimensionally unstable when their steepness exceeds 1/3.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 506 , 10 May 2004 , pp. 245 - 254
Copyright
© 2004 Cambridge University Press

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