Three-dimensional instability of axisymmetric flow in a rotating lid–cylinder enclosure
Three-dimensional instability of axisymmetric flow in a rotating lid–cylinder enclosure
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DOI：
10.1017/s0022112001004566
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发表时间：
2001-07
影响因子：
3.7
通讯作者：
A. Gelfgat;P. Bar-Yoseph;A. Solan
中科院分区：
文献类型：
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作者：
A. Gelfgat;P. Bar-Yoseph;A. Solan
本文分析了旋转盖与静止圆柱间轴对称流动的轴对称破缺三维不稳定性。流动由两个参数控制-雷诺数Re和纵横比γ（=高度/半径）。已发表的实验结果表明，在不同的γ范围内，可以观察到轴对称或非轴对称不稳定性。以前的分析只考虑轴对称不稳定性。本文分析了基本轴对称流在非轴对称扰动下的线性稳定性。线性化后的稳定性问题分解成一个家庭的准轴对称子问题的方位波数k的离散值。计算采用整体Galerkin方法。稳定性分析是在γ值在1 ~ 2.76范围内的各种密集分布下进行的，失稳是三维的，分别在k = 2和k = 3或4时发生。讨论了主扰动的方位周期性、模式、特征频率和相速度。
The axisymmetry-breaking three-dimensional instability of the axisymmetric flow between a rotating lid and a stationary cylinder is analysed. The flow is governed by two parameters – the Reynolds number Re and the aspect ratio γ (=height/radius). Published experimental results indicate that in different ranges of γ axisymmetric or non-axisymmetric instabilities can be observed. Previous analyses considered only axisymmetric instability. The present analysis is devoted to the linear stability of the basic axisymmetric flow with respect to the non-axisymmetric perturbations. After the linearization the stability problem separates into a family of quasi-axisymmetric subproblems for discrete values of the azimuthal wavenumber k. The computations are done using the global Galerkin method. The stability analysis is carried out at various densely distributed values of γ in the range 1 2.76, the instability is three-dimensional and sets in with k = 2 and k = 3 or 4, respectively. The azimuthal periodicity, patterns, characteristic frequencies and phase velocities of the dominant perturbations are discussed.