Bifurcation Phenomena and Transient Dynamics of the Flow between Rotating Cylinders with Finite Length

对旋转圆柱间的流动、发展和分叉现象进行了数值研究。研究了旋转圆盘的绕流和圆柱的绕流。在圆柱体的情况下，我们集中我们的注意力与自由表面和初始速度波动的流动。自由表面模型除了重力效应外，还考虑了表面张力的效应。离心力的作用首先出现在自由表面，然后Ekman层开始在静止的下端壁发展。最后的流型，包括表面波的结构，表现出良好的协议与实验观察。在实验中，不可避免地会出现物理误差。考虑到这些事实，我们在初始条件下引入准各向同性流，并研究其对流动发展的影响。通过对粘性尺度的测量，估算了初始速度的强度.数值结果表明，最终的流动模式很大程度上取决于初始强度，几乎所有的流动模式观察到的实验预测。在圆柱封闭腔内旋转圆盘绕流的研究中，考察了圆盘边缘与封闭腔内壁之间的差距内的不稳定流动。结果表明，差距内的不稳定流动使整个流动发生了剧烈的变化，并阐明了随雷诺数增加的分叉图。

Numerical studies were carried out on the flow, development and bifurcation phenomena in the flow between rotating cylinders. The flows around a rotating disc, as well as flows around circular cylinders, were investigated. In the case of the circular cylinders, we focused our attention on flows with free surface and initial fluctuations of velocity. The free surface model represented the effect of the surface tension in addition to the gravitational effect. The effect of the centrifugal force appears firstly at the free surface, and then the Ekman layer begins to develop on the stationary lower end wall. The final flow pattern, including the structure of the surface waves, showed good agreement with the experimental observation. In experiments, inevitable sources of physical errors appears. Considering these facts, we introduced quasi-isotropic flows in initial conditions and investigated their effects on flow developments. The intensity of the initial velocities~ were estimated by measuring the viscous scale. The numerical results showed that the final flow mode largely depended on the initial intensities and almost all the flow modes observed by experiments were predicted. In the study on flows around a rotating disc in a cylindrical enclosure, unstable flows in the gap between the rim of the disc and the inner wall of the enclosure were examined. It was shown that the unstable flow in the gap drastically changed the entire flow, and the bifurcation diagram with the increase in the Reynolds number was clarified.