Sequential transitions of bathtub vortex flow
Sequential transitions of bathtub vortex flow
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浴缸涡流的顺序转变
DOI：
10.1103/physrevfluids.2.083903
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发表时间：
2017
影响因子：
2.7
通讯作者：
Kazuki Abe and Naoto Yokoyama
中科院分区：
文献类型：
--
作者：
Jiro Mizushima;Kazuki Abe and Naoto Yokoyama
发现浴缸漩涡是由于排水时矩形容器内对称流动的不稳定性而自发产生的。通过数值模拟和线性稳定性分析，研究了具有矩形水平截面和底部中心有排水孔的容器的模型流动，研究了浴缸漩涡等旋转流体运动产生的物理机制和流动的顺序转变。即使在不稳定之后，水面也被假定为平坦的。如果在此假设下流动变得不稳定，则确保表面变形与不稳定无关。它强调，我们的兴趣不仅限于真正的浴缸漩涡，而是针对具有两个反射对称性的流动中出现的大漩涡。容器的外形具有双平面对称性(DPS)，这使得流动在较小的雷诺数时具有相同的DPS。结果表明，伴随着流场的对称性破缺，出现了不稳定性，从而发生了相变。也就是说，在临界雷诺数以上，DPS流动经历了不稳定而产生涡旋运动，失去了DPS，但保持了围绕中心轴的-旋转(两次旋转)对称性。在较高的雷诺数下，涡流也变得不稳定，发生转变，失去-旋转对称性，但仍保持时间平移对称性，即定常。在更高的雷诺数下，由于扰动的振荡模式引起的不稳定性，稳定性被破坏。流动的第一个和第二个转变被识别为干叉分叉，第三个转变被识别为Hopf分叉。
The bathtub vortex has been found to autonomously arise owing to instability of a symmetric flow in a rectangular vessel when water is drained. We consider a model flow through a vessel with a rectangular horizontal cross section and a drain hole at the center of the bottom to investigate the physical mechanism for generation of swirling fluid motion like the bathtub vortex and the sequential transitions of the flow by numerical simulations and the linear stability analyses. The water surface is assumed to be flat even after instability. If the flow becomes unstable under this assumption, it assures that the surface deformation is irrelevant to the instability. It is emphasized that our interest is not limited to the real bathtub vortex but directed to occurrence of a large vortex in a flow having two reflectional symmetries. The configuration of the vessel has the double plane symmetry (DPS), which allows the flow have the same DPS at small Reynolds numbers. It is found that the instabilities and hence transitions occur accompanying symmetry-breaking of the flow field. Namely, the DPS flow experiences instability to yield vortical motion above a critical Reynolds number, losing the DPS but retaining the-rotational (twofold rotational) symmetry around the center axis. The vortical flow also becomes unstable at a higher Reynolds number, makes a transition, and loses the-rotational symmetry, but still keeps the time-translation symmetry, i.e., steadiness. The steadiness is broken at an even higher Reynolds number, owing to instability caused by an oscillatory mode of disturbance. The first and second transitions of the flow are identified as pitchfork bifurcations, and the third transition is identified as a Hopf bifurcation.