Breakdown of self-similarity at the crests of large-amplitude standing water waves.
Breakdown of self-similarity at the crests of large-amplitude standing water waves.
复制标题
大振幅驻水波波峰处的自相似性破裂。
DOI：
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发表时间：
2010
影响因子：
8.6
通讯作者：
J. Wilkening
中科院分区：
文献类型：
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作者：
J. Wilkening
利用双精度和四倍精度的高分辨率数值模拟，研究了大振幅驻波在深水中的极限行为。当周期行波以一种渐近自相似的方式逼近Stokes尖峰极值波时，我们发现驻波的行为有所不同。与先前推测的那样磨到角落或尖端不同，波峰尖端形成了各种振荡结构。这导致将这些波参数化的分叉曲线分裂成与所发生的不同振荡模式相对应的不相交的分支。在许多情况下，垂直的流体射流将这些结构向上推，导致波浪池实验中常见的波形。因此，在之前被认为是自相似的体系中，我们在小尺度上观察到了丰富的动态行为。
We study the limiting behavior of large-amplitude standing waves on deep water using high-resolution numerical simulations in double and quadruple precision. While periodic traveling waves approach Stokes's sharply crested extreme wave in an asymptotically self-similar manner, we find that standing waves behave differently. Instead of sharpening to a corner or cusp as previously conjectured, the crest tip develops a variety of oscillatory structures. This causes the bifurcation curve that parametrizes these waves to fragment into disjoint branches corresponding to the different oscillation patterns that occur. In many cases, a vertical jet of fluid pushes these structures upward, leading to wave profiles commonly seen in wave tank experiments. Thus, we observe a rich array of dynamic behavior at small length scales in a regime previously thought to be self-similar.