Transverse Instability of Surface Solitary Waves and Breaking (Workshop on Nonlinear Water Waves)

Abstract

The linear stability of finite-amplitude surface solitary waves with respect to transverse perturbations (three-dimensional perturbations) is studied on the basis of the Euler set of equations. First, the linear stability to long-wavelength transverse perturbations is examined, and it is found that there exist transversely unstable surface solitary waves for the amplitude-to-depth ratio of over 0.713 (Kataoka& Tsutahara 2004). This critical ratio is well below that (=0.781) for the longitudinal instability obtained by Tanaka (1986). Next, the same transverse instability is examined numerically and we find that results are consistent with the above analytical results in that the growth rates and the eigenfunctions of growing disturbance modes agree well with those obtained by the theory (Kataoka 2010). Finally, time evolution of transversely distorted solitary wave is simulated numerically in order to give clear intuitive picture of unstable wave motion. In this report we only treat the fmal topic on numerical simulation of a distorted solitary wave since the first two topics were already published.