Exact coherent states in plane Couette flow under spanwise wall oscillation
Exact coherent states in plane Couette flow under spanwise wall oscillation
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DOI：
10.1017/jfm.2022.606
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发表时间：
2022-08
影响因子：
3.7
通讯作者：
Yacine Bengana;Qiang Yang;Guohua Tu;Y. Hwang
中科院分区：
文献类型：
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作者：
Yacine Bengana;Qiang Yang;Guohua Tu;Y. Hwang
摘要计算了沿展向壁面振荡控制下平面Couette流动中具有一定壁面振荡幅值和周期$({A_w}， T)$的几个精确相干态。研究发现，壁面振荡总体上稳定了平衡解的上支，实现了相应的减阻，而对下支的影响较小。在${T^{+}} \约为100$时，稳定效应随振荡幅值的增加而增加。精确的相干态再现了以往研究中观察到的条纹的一些关键动力学行为，同时显示了从湍流态的相位平均中无法提取的丰富的相干结构动力学。状态画像的可视化显示，支持湍流解的状态空间的大小被跨向壁面振荡减小，并且上分支平衡解变得不那么排斥，它们的许多不稳定流形被稳定。这种状态空间动力学的变化导致湍流寿命的显著减少。最后，精确相干状态的主要稳定机制被发现是抑制条纹的上升效应，解释了为什么以前的线性分析在湍流稳定建模和由此产生的阻力减少方面如此成功。
Abstract A set of several exact coherent states in plane Couette flow is computed under spanwise wall oscillation control, with a range of wall oscillation amplitudes and periods $({A_w}, T)$. It is found that the wall oscillation generally stabilises the upper branch of the equilibrium solutions and achieves the corresponding drag reduction, while it influences modestly the lower branch. The stabilisation effect is found to increase with the oscillation amplitude with an optimal time period around ${T^{+}} \approx 100$. The exact coherent states reproduce some key dynamical behaviours of streaks observed in previous studies, while exhibiting the rich coherent structure dynamics that cannot be extracted from a phase average of turbulent states. Visualisation of state portraits shows that the size of the state space supporting turbulent solution is reduced by the spanwise wall oscillation, and the upper-branch equilibrium solutions become less repelling, with many of their unstable manifolds being stabilised. This change of the state space dynamics leads to a significant reduction in lifetime of turbulence. Finally, the main stabilisation mechanism of the exact coherent states is found to be the suppression of the lift-up effect of streaks, explaining why previous linear analyses have been so successful for turbulence stabilisation modelling and the resulting drag reduction.