From Newton’s bucket to rotating polygons: experiments on surface instabilities in swirling flows
From Newton’s bucket to rotating polygons: experiments on surface instabilities in swirling flows
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从牛顿桶到旋转多边形：旋流中表面不稳定性的实验
DOI：
10.1017/jfm.2014.568
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发表时间：
2014
影响因子：
3.7
通讯作者：
Erik Linnartz
中科院分区：
文献类型：
--
作者：
Tomas Bohr;Bjarne Bach;M. Vested;Anders Andersen;Erik Linnartz
摘要：我们提出了一项关于在部分填充的圆柱形容器中旋转水流的自由表面上形成“多边形”的实验研究。在我们的设置中，我们用单独的电机旋转底板和气缸壁。因此，我们独立地改变旋转速率和剪切强度，并从刚性旋转的“牛顿桶”流转变为底部和圆柱壁反向旋转且表面强烈湍流但平均平坦的流。在这两个极端之间，我们发现旋转对称性自发破缺的多边形状态。我们研究了给定注水高度下两个旋转频率所跨越的相图，并找到了一个状态中的多边形，其中两个频率足够不同，并且主要是当它们具有相反的符号时。除了固定圆柱体发现的多边形族的扩展之外，我们还发现了一个新的较小多边形族，用于圆柱体的较大旋转速率，与底板的旋转速率相反。此外，我们还发现了一个“单边形”，一种有一个角的图形，大致是一个偏心圆，其旋转方向与圆柱体相同。仅底板旋转的情况与 Jansson 等人的结果进行了比较。 (Phys. Rev. Lett., vol. 96, 2006, art. 174502)，其中使用了相同尺寸的圆柱体，虽然由水高度和旋转频率跨越的相图的整体结构是相同的，但许多细节是不同的。为了测试小实验缺陷（例如底板未对准）的影响，我们研究了旋转多边形是否与底板锁相，尽管我们发现图形和底板的频率比接近合理的情况，但我们没有发现锁相。最后，我们表明该系统具有令人惊讶的多稳定性和兴奋性，并且我们注意到这可能会导致在可比实验中获得的相图之间存在定量差异。
Abstract We present an experimental study of ‘polygons’ forming on the free surface of a swirling water flow in a partially filled cylindrical container. In our set-up, we rotate the bottom plate and the cylinder wall with separate motors. We thereby vary rotation rate and shear strength independently and move from a rigidly rotating ‘Newton’s bucket’ flow to one where bottom and cylinder wall are rotating oppositely and the surface is strongly turbulent but flat on average. Between those two extremes, we find polygonal states for which the rotational symmetry is spontaneously broken. We investigate the phase diagram spanned by the two rotational frequencies at a given water filling height and find polygons in a regime, where the two frequencies are sufficiently different and, predominantly, when they have opposite signs. In addition to the extension of the family of polygons found with the stationary cylinder, we find a new family of smaller polygons for larger rotation rates of the cylinder, opposite to that of the bottom plate. Further, we find a ‘monogon’, a figure with one corner, roughly an eccentric circle rotating in the same sense as the cylinder. The case where only the bottom plate is rotating is compared with the results of Jansson et al. (Phys. Rev. Lett., vol. 96, 2006, art. 174502), where the same size of cylinder was used, and although the overall structure of the phase diagram spanned by water height and rotational frequency is the same, many details are different. To test the effect of small experimental defects, such as misalignment of the bottom plate, we investigate whether the rotating polygons are phase locked with the bottom plate, and although we find cases where the frequency ratio of figure and bottom plate is nearly rational, we do not find phase locking. Finally, we show that the system has a surprising multistability and excitability, and we note that this can cause quantitative differences between the phase diagrams obtained in comparable experiments.
影响因子：
4.6
作者：
Toshiyuki Suzuki;M. Iima;Y. Hayase
通讯作者：
Toshiyuki Suzuki;M. Iima;Y. Hayase