Transverse instability of surface solitary waves. Part 2. Numerical linear stability analysis

Author:

KATAOKA TAKESHI

Abstract

In a previous work, Kataoka & Tsutahara (J. Fluid Mech., vol. 512, 2004a, p. 211) proved the existence of longitudinally stable but transversely unstable surface solitary waves by asymptotic analysis for disturbances of small transverse wavenumber. In the present paper, the same transverse instability is examined numerically for the whole range of solitary-wave amplitudes and transverse wavenumbers of disturbances. Numerical results show that eigenvalues and eigenfunctions of growing disturbance modes agree well with those obtained by the asymptotic analysis if the transverse wavenumber of the disturbance is small. As the transverse wavenumber increases, however, the growth rate of the disturbance, which is an increasing function for small wavenumbers, reaches a maximum and finally falls to zero at some finite wavenumber. Thus, there is a high-wavenumber cutoff to the transverse instability. For higher amplitude, solitary waves become longitudinally unstable, and the dependence of the eigenvalues on the transverse wavenumber exhibits various complicated patterns. We found that such eigenvalues versus transverse wavenumber can be simply grouped into three basic classes.

Publisher

Cambridge University Press (CUP)

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Resonance theory of water waves in the long-wave limit;Journal of Fluid Mechanics;2013-03-28

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