In this study, the structure of the fluid flow and vortices are investigated for the circular Couette flow, Taylor vortex and wavy vortex regimes by changing the Womersley number and periods of oscillations of the inner cylinder rotation. The rotational velocity of the inner cylinder, \(\omega\), increases linearly with time from zero to a maximum value and then decreases to zero in a periodic manner. The Womersley number, Wo, varies between \(0.27 \le Wo \le 12.14,\) and the flow is assumed laminar. The results consist of two separate parts as the inner cylinder rotates with 1) positive and 2) negative accelerations. It is observed that by increasing Wo, the flow cannot follow the given boundary condition and there is a time delay. Therefore, the values of the critical Taylor number become different from those of the steady-state conditions. For Wo=0.27 and when the inner cylinder rotates with positive acceleration, the primary critical Taylor number is 40% higher than that of steady state, while as the inner cylinder rotates with negative acceleration, this is only 7.2% higher than the corresponding steady-state condition. It should be noted that for two values of the Womersley numbers, Wo=12.14 and Wo=8.59, no flow instability occurs and no vortex appears until the second period of the inner cylinder oscillations. The reason is that the timescale of the dynamics of flow is lower than the timescale of the flow instability; thus, the flow is circular Couette without any vortex.

在这项研究中，通过改变内圆柱体旋转的沃默斯利数和振荡周期，研究了圆形库埃特流、泰勒涡流和波浪涡流状态的流体流动和涡流的结构。内圆柱体的旋转速度\(\omega\)随时间线性增加，从零到最大值，然后以周期性方式减小到零。Womersley 数Wo在\(0.27 \le Wo \le 12.14,\)之间变化，并且假定流动为层流。结果由两个独立的部分组成，因为内圆柱体以 1) 正加速度和 2) 负加速度旋转。据观察，通过增加Wo，流不能遵循给定的边界条件，并且存在时间延迟。因此，临界泰勒数的值与稳态条件的值不同。对于Wo =0.27，当内筒以正加速度旋转时，主临界泰勒数比稳态高40%，而当内筒以负加速度旋转时，仅比相应的稳态高7.2%。状态。需要注意的是，对于 Womersley 数的两个值，Wo = 12.14 和Wo=8.59，直到内圆柱振荡的第二个周期才出现流动不稳定并且没有涡流出现。原因是流动动力学的时间尺度低于流动不稳定的时间尺度；因此，流动是圆形的库埃特，没有任何涡流。