Bifurcations and instabilities in sliding Couette flow
Bifurcations and instabilities in sliding Couette flow
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DOI：
10.1017/jfm.2011.103
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发表时间：
2011-04
影响因子：
3.7
通讯作者：
K. Deguchi;M. Nagata
中科院分区：
文献类型：
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作者：
K. Deguchi;M. Nagata
本文对两个半径为a和B的无限长同心圆柱之间的流动进行了线性和非线性分析，内圆柱作轴向滑动运动。我们证实了Gittler（Acta Mechanica，vol.101，1993，p.1）关于轴对称情况的线性稳定性结果，即当半径比η = a/B大于0.1415时，流动对轴对称扰动是线性稳定的。我们把他的分析推广到非轴对称的情况，发现流动的稳定性仍然是由轴对称扰动决定的。我们的非线性分析表明：（i）有限振幅轴对称解存在远低于线性临界雷诺数η 0.1415，其中线性临界状态不存在。
We carry out linear and nonlinear analyses on a flow between two infinitely long concentric cylinders with the radii a and b subject to a sliding motion of the inner cylinder in the axial direction. We confirm the linear stability result of Gittler (Acta Mechanica, vol. 101, 1993, p. 1) for the axisymmetric case, namely the flow is linearly stable against axisymmetric perturbations when the radius ratio η = a/b is greater than 0.1415. We extend his analysis to the non-axisymmetric case and find that the stability of the flow is still determined by axisymmetric perturbations. Our nonlinear analysis exhibits that (i) finite-amplitude axisymmetric solutions exist far below the linear critical Reynolds number for η 0.1415 where the linear critical state is absent.