Using spatiotemporal linear stability theory, we conduct a systematic study of confined countercurrent shear layer velocity profiles, using realistic velocity profiles that capture the effects of wall boundary layers on canonical profile shapes. It is shown, in line with previous studies, that additional unstable modes are generated when confining walls are present. This leads to shifts in the absolute-convective transition boundary, with the effects being dramatic when confinement is on the high-speed side. However, over large parts of the parameter space, as specified by the counterflow parameter $R$ and the degree of confinement ($H$, measured in terms of shear layer momentum thickness), these correspond to long wave modes. It is shown that as counterflow parameter $R$ ($=\frac{U_1-U_2}{U_1+U_2}$, $U_1$ and $U_2$ being primary and secondary velocity streams) is increased to large values, the confined mode gradually decreases in wavelength. Comparisons of the behavior of the frequency of this confined mode are made with observed peak frequencies from the first experimental realization of momentum-driven confined countercurrent shear layers, and the results are shown to be in reasonable agreement.

中文翻译：

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约束对动量驱动逆流剪切层绝对和对流不稳定性的影响

使用时空线性稳定性理论，我们对受限逆流剪切层速度剖面进行系统研究，使用真实的速度剖面来捕捉壁边界层对规范剖面形状的影响。结果表明，与先前的研究一致，当存在限制壁时会产生额外的不稳定模式。这会导致绝对对流过渡边界的变化，当限制在高速侧时效果会非常显着。然而，在参数空间的很大一部分上，如逆流参数所指定的$\mathrm{电阻}$ 和限制的程度（$H$，根据剪切层动量厚度测量），这些对应于长波模式。表明作为逆流参数$\mathrm{电阻}$ ($=\frac{{你}_1-{你}_2}{{你}_1+{你}_2}$, ${你}_1$ 和 ${你}_2$主要和次要速度流）增加到大值，限制模式的波长逐渐减小。这种受限模式的频率行为与从动量驱动受限逆流剪切层的第一次实验实现中观察到的峰值频率进行了比较，结果显示出合理的一致性。