Hydroelastic solitary waves in deep water
Hydroelastic solitary waves in deep water
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DOI：
10.1017/jfm.2011.163
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发表时间：
2011-07-01
影响因子：
3.7
通讯作者：
Wang, Zhan
中科院分区：
文献类型：
--
作者：
Milewski, Paul A.;Vanden-Broeck, J-M.;Wang, Zhan
本文用渐近方法和数值方法研究了波在无限深二维理想流体表面上的传播问题。我们使用一个非线性弹性模型，已被用来描述冰盖的动力学。特别注意的是强迫和非强迫的波具有接近最小相速度的动态。对于非受迫问题，我们发现波包孤立波从最小速度的非线性周期波分叉。当问题是被迫由移动负载，我们发现，对于小振幅强迫，稳定的响应是可能的，在所有亚临界速度，但对于较大的负载有一个跨临界范围的强迫速度，没有稳定的解决方案。在非定常计算中，我们发现，如果问题是被迫在这个范围内的速度，得到非常大的非定常响应，当强迫被释放，孤立波产生。这些孤立波看起来很稳定，并且可以在小振幅波的海洋中共存。
The problem of waves propagating on the surface of a two-dimensional ideal fluid of infinite depth bounded above by an elastic sheet is studied with asymptotic and numerical methods. We use a nonlinear elastic model that has been used to describe the dynamics of ice sheets. Particular attention is paid to forced and unforced dynamics of waves having near-minimum phase speed. For the unforced problem, we find that wavepacket solitary waves bifurcate from nonlinear periodic waves of minimum speed. When the problem is forced by a moving load, we find that, for small-amplitude forcing, steady responses are possible at all subcritical speeds, but for larger loads there is a transcritical range of forcing speeds for which there are no steady solutions. In unsteady computations, we find that if the problem is forced at a speed in this range, very large unsteady responses are obtained, and that when the forcing is released, a solitary wave is generated. These solitary waves appear stable, and can coexist within a sea of small-amplitude waves.