调制不稳定深水表面重力波的不完全重现
On the incomplete recurrence of modulationally unstable deep-water surface gravity waves
摘要：
在完全非线性位流欧拉方程的框架内，讨论了调制不稳定水波列的重现问题。特别地，检查是否从任何地方出现的调制（即，最初是无穷小的），并产生一个流氓波，然后消失无踪。如果是这样的话，这个波解将是原始流体动力学方程的呼吸者解。它示出的帮助下的完全非线性数值模拟，当流氓波发生从一个均匀的斯托克斯波列，它激发其他波具有不同的长度，防止完全复发，并最终导致在一个准周期呼吸的波包络。同时，所发现的效应在幅度上相当小，调制呼吸的周期可能是主波周期的数千倍。因此，所得到的解可称为欧拉方程的拟呼吸子。
英文摘要：
The issue of a recurrence of the modulationally unstable water wave trains within the framework of the fully nonlinear potential Euler equations is addressed. It is examined, in particular, if a modulation which appears from nowhere (i.e., is infinitesimal initially) and generates a rogue wave which then disappears with no trace. If so, this wave solution would be a breather solution of the primitive hydrodynamic equations. It is shown with the help of the fully nonlinear numerical simulation that when a rogue wave occurs from a uniform Stokes wave train, it excites other waves which have different lengths, what prevents the complete recurrence and, eventually, results in a quasi-periodic breathing of the wave envelope. Meanwhile the discovered effects are rather small in magnitude, and the period of the modulation breathing may be thousands of the dominant wave periods. Thus, the obtained solution may be called a quasi-breather of the Euler equations.
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