The local and global stability of confined planar wakes at intermediate Reynolds number
The local and global stability of confined planar wakes at intermediate Reynolds number
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DOI：
10.1017/jfm.2011.324
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发表时间：
2011-09
影响因子：
3.7
通讯作者：
M. Juniper;O. Tammisola;F. Lundell
中科院分区：
文献类型：
--
作者：
M. Juniper;O. Tammisola;F. Lundell
摘要 在高雷诺数下，当尾流被限制在管道内或两个平板之间时，它们会变得更加不稳定。然而，当雷诺数约为 100 时，全球分析表明，这种流动在受到限制时会变得更加稳定，而局部分析表明，它们会变得更加不稳定。本文的目的是通过研究一组无障碍尾流来解决这个明显的矛盾。在这项理论和数值研究中，我们结合了 $\mathit{Re}= 100$ 处平面尾流的全局和局部稳定性分析来确定约束的影响。我们发现限制以三种方式起作用：它改变再循环区的长度（如果存在），它使边界层更接近剪切层，并且它可以使流动更加局部绝对不稳定。根据流动参数的不同，这些效应会相互作用或相互对抗，从而使流动不稳定或稳定。在具有自由滑移边界的 $\mathit{Re}= 100$ 的尾流中，当外部流比内部流的半宽宽 50 % 时，流动是全局最不稳定的，因为第一和第三效应共同作用。在 $\mathit{Re}= 100$ 且无滑移边界的尾流中，当流动弱约束时，约束几乎没有总体影响，因为前两个影响与第三个影响相反。然而，当流动受到强烈限制时，限制具有很强的稳定作用，因为所有三种效应共同作用。通过结合局部和全局分析，我们已经能够分离出这三种影响并解决以前工作中的明显矛盾。
Abstract At high Reynolds numbers, wake flows become more globally unstable when they are confined within a duct or between two flat plates. At Reynolds numbers around 100, however, global analyses suggest that such flows become more stable when confined, while local analyses suggest that they become more unstable. The aim of this paper is to resolve this apparent contradiction by examining a set of obstacle-free wakes. In this theoretical and numerical study, we combine global and local stability analyses of planar wake flows at $\mathit{Re}= 100$ to determine the effect of confinement. We find that confinement acts in three ways: it modifies the length of the recirculation zone if one exists, it brings the boundary layers closer to the shear layers, and it can make the flow more locally absolutely unstable. Depending on the flow parameters, these effects work with or against each other to destabilize or stabilize the flow. In wake flows at $\mathit{Re}= 100$ with free-slip boundaries, flows are most globally unstable when the outer flows are 50 % wider than the half-width of the inner flow because the first and third effects work together. In wake flows at $\mathit{Re}= 100$ with no-slip boundaries, confinement has little overall effect when the flows are weakly confined because the first two effects work against the third. Confinement has a strong stabilizing effect, however, when the flows are strongly confined because all three effects work together. By combining local and global analyses, we have been able to isolate these three effects and resolve the apparent contradictions in previous work.