On spatially growing disturbances in an inviscid shear layer
On spatially growing disturbances in an inviscid shear layer
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DOI：
10.1017/s0022112065001520
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发表时间：
1965-11
影响因子：
3.7
通讯作者：
A. Michalke
中科院分区：
文献类型：
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作者：
A. Michalke
剪切层失稳的实验研究表明，一些明显的失稳性质的基本特征不能用随时间增长扰动的无粘线性化稳定性理论来描述。因此，利用空间增长扰动的无粘线性化稳定性理论，试图得到与实验结果较吻合的结果。利用双曲切线速度剖面对复波数和实频率的特征值和特征函数进行了数值计算。所得结果与实验结果一致。利用计算得到的涡度分布和计算得到的条纹线，讨论了扰动流的物理性质。研究发现，受扰动剪切层以复杂的方式卷起。进一步，对线性化理论的有效性进行了估计。结果表明，扰动方程的线性化误差在涡度分布下应大于速度分布下，在高扰动频率下应大于低扰动频率下。最后，将实验结果与Freymuth的时空理论进行比较，可以得出这样的结论：空间生长扰动理论更准确地描述了扰动剪切层的不稳定性，至少在小频率下是如此。
Experimental investigations of shear layer instability have shown that some obviously essential features of the instability properties cannot be described by the inviscid linearized stability theory of temporally growing disturbances. Therefore an attempt is made to obtain better agreement with experimental results by means of the inviscid linearized stability theory of spatially growing disturbances. Thus using the hyperbolic-tangent velocity profile the eigenvalues and eigenfunctions were computed numerically for complex wave-numbers and real frequencies. The results so obtained showed the tendency expected from the experiments. The physical properties of the disturbed flow are discussed by means of the computed vorticity distribution and the computed streaklines. It is found that the disturbed shear layer rolls up in a complicated manner. Furthermore, the validity of the linearized theory is estimated. The result is that the error due to the linearization of the disturbance equation should be larger for the vorticity distribution than for the velocity distribution, and larger for higher disturbance frequencies than for lower ones. Finally, it can be concluded from the comparison between the results of experiments and of both the spatial and temporal theory by Freymuth that the theory of spatially-growing disturbances describes the instability properties of a disturbed shear layer more precisely, at least for small frequencies.