On the transition of transient growth mechanism in Taylor–Dean flow
On the transition of transient growth mechanism in Taylor–Dean flow
复制标题
泰勒·迪安流瞬态增长机制的转变
DOI：
10.1142/s0217984921501852
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发表时间：
2021-02
影响因子：
1.9
通讯作者：
Wei Zhang
中科院分区：
文献类型：
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作者：
Cheng Chen;Liu Zhang;Wei Zhang
从理论上研究了Taylor-Dean流中的最优摄动及其瞬时增长特性。描述由方位向压力梯度引起的平均泵送速度与旋转圆筒旋转速度之比的参数[公式：见正文]从−5变化到5。结果表明，对于刚性旋转情况，最优摄动的能量增长随着方位压力梯度的增大而增加。此外，在宽间隙情况下，方位速度幅值的主峰和次峰都向外筒方向移动，而在窄间隙情况下，方位速度幅值的主峰和次峰向内柱相反移动。从三个速度分量的能量随时间的演化来看，当[公式]从−5变为5时，反提离机制取代提离机制成为能量增长的主导机制。而对于窄缝隙情况，无论方位压力梯度有多大，提离机制始终是轴对称扰动的瞬时增长的原因。
We investigate optimal perturbation and its transient growth characteristics in Taylor–Dean flow theoretically. The parameter [Formula: see text], accounting for the ratio of average pumping velocity induced by azimuthal pressure gradient to rotating velocity by rotating cylinders, is varied from −5 to 5. The results show that for the rigid rotation case, the energy growth of optimal perturbation is increased with increasing magnitude of azimuthal pressure gradient. Further, both the main and secondary peak of the amplitude of azimuthal velocity are seen to be shifted towards the outer cylinder for wide gap case, and both are shifted oppositely towards the inner cylinder for narrow gap case. Viewing the time evolution of the energies in the three velocity components for wide gap case, anti-lift-up mechanism replaces lift-up mechanism as the dominant mechanism for energy growth, when [Formula: see text] changes from −5 to 5. While for narrow gap case, lift-up mechanism is always responsible for transient growth of axisymmetric perturbation, no matter how strong azimuthal pressure gradient is considered.