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

对旋转圆柱间流动的流动、发展和分岔现象进行了数值研究。研究了旋转圆盘周围的流动和圆柱周围的流动。在圆柱的情况下，我们把注意力集中在具有自由表面和初始速度波动的流动上。自由表面模型除考虑重力效应外，还考虑了表面张力的影响。离心力的作用首先出现在自由表面，然后在静止的下端壁上开始形成埃克曼层。最终的流态，包括表面波的结构，与实验观测结果吻合良好。在实验中，不可避免地会出现物理误差的来源。考虑到这些事实，我们在初始条件下引入了准各向同性流动，并研究了它们对流动发展的影响。通过对粘性尺度的测量，估计了初始速度的强度。数值计算结果表明，最终的流动模式在很大程度上取决于初始强度，并且几乎所有实验观察到的流动模式都可以预测。在圆柱壳体内旋转圆盘的流动研究中，研究了圆盘边缘与壳体内壁间隙内的不稳定流动。结果表明，间隙内的不稳定流动极大地改变了整个流动，并明确了随雷诺数增加的分岔图。

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.