On wavy instabilities of the Taylor-vortex flow between corotating cylinders
On wavy instabilities of the Taylor-vortex flow between corotating cylinders
复制标题
共转圆柱间泰勒涡流的波状不稳定性
DOI：
10.1017/s0022112088000862
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发表时间：
1988
影响因子：
3.7
通讯作者：
M. Nagata
中科院分区：
文献类型：
--
作者：
M. Nagata
本文通过分析同向差动旋转的两同心圆柱之间的小间隙内泰勒涡流（TVF）的线性稳定性，用数值方法发现至少有四种波动不稳定性。两个波动的不稳定性，包括一个导致传统的波动涡（WVF），具有相同的轴向波长TVF在发病的不稳定性，而其他两个的特点是由亚谐波模式的轴向波长的两倍长的TVF。这两种亚谐不稳定性似乎对应于Andereck，Liu & Swinney（1986）实验中观察到的波动流入边界流（WIB）和波动流出边界流（WOB）。在旋转坐标系中测得的所有波动不稳定性的相速度在开始时都是非零的，除了WVF的相速度在圆柱的平均旋转速率Ω较小的区域为零。利用WVF在小Ω时的这种简单分叉特性，数值跟踪了从TVF分叉出来的与时间无关的有限振幅非轴对称解分支。最有趣的发现是，一些解分支穿过线Ω = 0，在平面Couette流中产生三维非线性解。
At least four wavy instabilities are found numerically by analysing the linear stability of Taylor-vortex flow (TVF) in the limit of a small gap between two concentric cylinders which rotate differentially in the same direction. Two of the wavy instabilities, including the one leading to conventional wavy vortex (WVF), have the same axial wavelength as TVF at the onset of instability, while the other two are characterized by subharmonic modes with axial wavelengths twice as long as those of TVF. The two subharmonic instabilities appear to correspond to the wavy-inflow-boundary flow (WIB) and the wavy-outflow-boundary flow (WOB) observed in the experiment of Andereck, Liu & Swinney (1986). The phase velocities, measured in the rotating frame of reference, of all the wavy instabilities are non-zero at the onset except that the phase velocity of WVF vanishes in the region where the average rotation rate Ω of the cylinders is small. By using this simple bifurcation property of WVF for small Ω, time-independent finite-amplitude non-axisymmetric solution branches bifurcating from TVF are followed numerically. The most interesting findings are that some of the solution branches cross the line Ω = 0, producing three-dimensional nonlinear solutions in plane Couette flow.