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Transverse instability of surface solitary waves

Published online by Cambridge University Press:  23 July 2004

T. KATAOKA  and
M. TSUTAHARA
T. KATAOKA
Affiliation:
Graduate School of Science and Technology, Kobe University, Rokkodai, Nada, Kobe 657-8501, Japan
M. TSUTAHARA
Affiliation:
Graduate School of Science and Technology, Kobe University, Rokkodai, Nada, Kobe 657-8501, Japan
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Abstract

The linear stability of finite-amplitude surface solitary waves with respect to long-wavelength transverse perturbations is examined by asymptotic analysis for small wavenumbers of perturbations. The sufficient condition for the transverse instability is explicitly derived, and it is found that there exist transversely unstable surface solitary waves whose amplitude-to-depth ratio is greater than 0.713. This critical ratio is well below that for the one-dimensional instability (${=}\,0.781$) obtained by Tanaka (Phys. Fluids, 1986, vol. 29, p. 650).

Type
Papers
Information
Journal of Fluid Mechanics , Volume 512 , 10 August 2004 , pp. 211 - 221
Copyright
© 2004 Cambridge University Press

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