剪切层与边界层组合流动的线性不稳定性分析

对不可压缩剪切层与边界层的组合流动完成了线性稳定性研究.组合流动的数学模型为Blasius边界层相似解与双曲正切函数的叠加，采用整体数值方法求解组合流动的稳定性方程，并验证了程序的准确性及网格无关性.研究给出组合流动的不稳定模态的辨识，即边界层模态和剪切层模态.在此基础上研究了剪切层对边界层模态不稳定性的影响以及壁面对剪切层模态的影响.由于剪切层的存在，使边界层模态中性曲线向左上方平移，临界雷诺数减小.此外，边界层模态不稳定性得到增强或抑制的影响，取决于扰动频率以及剪切层速度比的变化.组合流动中壁面边界层促使剪切层不稳定性减弱，主要表现在低频区域；而在高频区域，剪切层不稳定性几乎不受壁面边界层的影响. 

Linear instability analysis of the confluent shear layer and boundary layer flows

The linear stability theory (LST) was used to study the confluent shear layer/boundary layer flows. The mean velocity profile exhibited a superposition of the Blasius boundary layer and a shear layer expressed as hyperbolic tangent function. A global method with high order difference schemes was used to solve the Orr-Sommerfeld equation. The numerical procedure was validated by comparing the present results for boundary layer and shear layer with the published articles. The unstable wave modes associated with both shear layer and boundary layer were identified. On this basis, the interactions between the boundary layer mode and the shear layer were examined. Due to the presence of the shear layer, the neutral curve of the boundary layer mode moved to the upper left, resulting in decrease of critical Reynolds number. When the shear layer was brought close to the wall, the boundary layer unstable mode may be destabilized or stabilized, depending upon the disturbance frequency. In the confluent flow, the wall boundary layer has a stabilized effect on the shear layer mode, which occurs in the low frequency range.