Discrete modes and continuous spectra in supersonic boundary layers
Discrete modes and continuous spectra in supersonic boundary layers
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DOI：
10.1017/s0022112092004555
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发表时间：
1992-06
影响因子：
3.7
通讯作者：
By P. Balakumar;M. Malik
中科院分区：
文献类型：
--
作者：
By P. Balakumar;M. Malik
谐波点源引起的扰动场由离散本征模和连续谱组成，利用广义傅里叶变换技术对其进行了研究。对于超声速边界层，在复波数空间中存在七个连续谱分支，其中四个（两个声波、一个涡量波和一个熵波）对源下游流场有贡献。在某些临界雷诺数下，离散的本征模从这些分支中跳脱。对马赫数为2和4.5的边界层的计算结果表明，稳定离散模态的感受性系数远大于不稳定模态。因此，非常靠近源的流动由连续谱和稳定的离散模式主导。然而，不稳定模式在离源足够远的地方接管。结果表明，它是只需要考虑前几个离散模式构造的解决方案。计算还表明，在超音速边界层中，局部扰动对上游的影响是最小的。
The disturbance field induced due to a harmonic point source consists of discrete eigenmodes and a continuous spectrum; these are studied by using generalized Fourier transform techniques. For a supersonic boundary layer, there exist seven branches of the continuous spectrum in the complex wavenumber space, four of which (two acoustic waves, one vorticity wave and one entropy wave) contribute to the flow field downstream of the source. The discrete eigenmodes spring off from these branches at some critical Reynolds numbers. The results for Mach 2 and 4.5 boundary layers show that the receptivity coefficients for the stable discrete modes are much larger than that for the unstable mode. Therefore, the flow very near the source is dominated by the continuous spectrum and the stable discrete modes. However, the unstable mode takes over sufficiently far away from the source. It is shown that it is only necessary to consider the first few discrete modes to construct the solution. Calculations also show that, in a supersonic boundary layer, upstream influence from a localized disturbance is minimal.