In this paper, the influence of the Mach number on the stability of two-dimensional compressible planar wakes is studied to gain physical insight into the turbine wakes. Two-dimensional instabilities of compressible wakes are studied using local spatiotemporal instability analyses. The absolute/convective boundary of a family of wake profiles is obtained at different Mach numbers. Then, local stability analyses of compressible wakes behind flat plates are performed. It is found that in the subsonic region increasing Mach number acts in two ways to modify the instability characteristics in the near wake region: it lengthens the recirculation zone and it reduces the absolute growth rate. These two mechanisms work against each other, which explains why the linear global growth rate varies slightly as Mach number changes in the subsonic region. Further increasing Mach number to 1 would greatly reduce the length of the absolute unstable region due to the occurrence of expansion waves around the trailing edge corner. As a result, the wake is strongly stabilized at $$\hbox {Ma}=1$$ Ma = 1 .

中文翻译：

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马赫数对可压缩平面尾流绝对/对流稳定性的影响

在本文中，研究了马赫数对二维可压缩平面尾流稳定性的影响，以获得对涡轮尾流的物理洞察。使用局部时空不稳定性分析来研究可压缩尾流的二维不稳定性。一系列尾流剖面的绝对/对流边界是在不同的马赫数下获得的。然后，对平板后面的可压缩尾流进行局部稳定性分析。研究发现，在亚音速区域，增加马赫数以两种方式改变近尾流区域的不稳定性特征：延长再循环区和降低绝对增长率。这两种机制相互对抗，这就解释了为什么线性全球增长率随着亚音速区域马赫数的变化而略有不同。进一步将马赫数增加到 1 将大大减少由于后缘角周围出现膨胀波而导致的绝对不稳定区域的长度。结果，尾流强烈稳定在 $$\hbox {Ma}=1$$ Ma = 1 。