Survey of instability thresholds of flow between exactly counter-rotating disks
Survey of instability thresholds of flow between exactly counter-rotating disks
复制标题
精确反向旋转圆盘之间流动不稳定阈值的调查
DOI：
10.1017/s0022112004008559
复制
发表时间：
2004
影响因子：
3.7
通讯作者：
L. Tuckerman
中科院分区：
文献类型：
--
作者：
C. Nore;M. Tartar;O. Daube;L. Tuckerman
用数值方法研究了完全反向旋转盘间轴对称流动的三维线性不稳定性。动力学由两个参数控制：基于圆柱半径和圆盘转速的雷诺数$Re$和高半径比$\Gamma$。对$0.5 \,{\le}\, \Gamma \,{\le}\, 3$进行的稳定性分析表明，非轴对称模态占主导地位且平稳，临界方位角波数是$\Gamma$的递减函数。分析了主导扰动的模式，并讨论了与剪切层不稳定有关的物理机制。当$m\,{=}\,2$阈值先于$m\,{=}\,1$阈值时，在1:2协维点附近没有看到复杂动力学行为的证据。轴对称不稳定性也进行了计算；这些可能是平稳分岔或Hopf分岔。它们的阈值总是高于非轴对称模态的阈值。
The three-dimensional linear instability of axisymmetric flow between exactly counter-rotating disks is studied numerically. The dynamics are governed by two parameters, the Reynolds number $Re$ based on cylinder radius and disk rotation speed and the height-to-radius ratio $\Gamma$. The stability analysis performed for $0.5 \,{\le}\, \Gamma \,{\le}\, 3$ shows that non-axisymmetric modes are dominant and stationary and that the critical azimuthal wavenumber is a decreasing function of $\Gamma$. The patterns of the dominant perturbations are analysed and a physical mechanism related to a shear layer instability is discussed. No evidence of complex dynamical behaviour is seen in the neighbourhood of the 1:2 codimension-two point when the $m\,{=}\,2$ threshold precedes that of $m\,{=}\,1$. Axisymmetric instabilities are also calculated; these may be stationary or Hopf bifurcations. Their thresholds are always higher than those of non-axisymmetric modes.