The Froude number for solitary water waves with vorticity
The Froude number for solitary water waves with vorticity
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具有涡度的孤立水波的弗劳德数
DOI：
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发表时间：
2014
影响因子：
3.7
通讯作者：
Miles H. Wheeler
中科院分区：
文献类型：
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作者：
Miles H. Wheeler
考虑任意涡度分布的剪切流上的二维孤立水波。假设流体中的水平速度永远不会超过波速，并且自由表面在其渐近水平以上的任何地方，我们给出了一个非常简单的证明，即适当定义的弗劳德数必须严格大于临界值F=1。我们还证明了在更严格的涡度假设下F$的上界，从而证明了振幅的上界。
We consider two-dimensional solitary water waves on a shear flow with an arbitrary distribution of vorticity. Assuming that the horizontal velocity in the fluid never exceeds the wave speed and that the free surface lies everywhere above its asymptotic level, we give a very simple proof that a suitably defined Froude number $F$ must be strictly greater than the critical value $F=1$ . We also prove a related upper bound on $F$ , and hence on the amplitude, under more restrictive assumptions on the vorticity.