Streak Instability and Bypass Transition

层流-湍流转变是流体力学中的一个基本问题，它对阻力预测、气动加热和流动分离有着重要的意义。例如，过渡到湍流可以绕过压缩机中的流动分离，而在低压涡轮阶段，50%的流动可以是过渡的。虽然端态可能始终是一个平衡的湍流边界层，但转变本身可以通过不同的机制进行调节，并且每种机制都会导致明显不同的转变位置和长度。文献一般将过渡情景分为自然或有序的路线和旁路机制。前者以粘性Tollmien-Schlichting(T-S)不稳定波为特征，可以在安静的试验条件下通过实验观察到。在存在自由流扰动(大致称为自由流湍流(FST))的情况下，过渡发生得更快，因此绕过了自然路线，因此术语为旁路过渡。在旁路机制中，在流动的过渡前区域观察到拉长的高幅度扰动，称为边界层条纹。击穿被归因于这些条纹的二次不稳定，但确切的相关性仅被推测，从未令人满意地量化。该研究首次采用理论和数值相结合的方法，准确、高效地计算出了非线性条纹。我们还将分析这些条纹的稳定性，我们的研究将提供条纹不稳定性所需的自由流扰动阈值的估计。它还将给出条纹最先变得不稳定的位置和自由流扰动强度之间的定量关系。这些信息将对在过渡流区运行的翼型的设计有用。

Laminar-turbulent transition is a fundamental problem in fluid mechanics that has great implications for the prediction of drag, aerodynamic heating, and flow separation. For example, transition to turbulence can bypass flow separation in compressors, and in the low-pressure-turbine stage, 50% of the flow can be transitional. While the end-state may always be an equilibrium turbulent boundary layer, transition itself can be mediated by different mechanisms and each results in distinctly different transition locations and lengths. The literature generally divides transition scenarios into the natural, or orderly, route and the bypass mechanism. The former is characterized by viscous Tollmien-Schlichting (T-S) instability waves which can be observed experimentally under quiet testing conditions. In the presence of free-stream disturbances, which are loosely referred to as free-stream turbulence (FST), transition takes place more swiftly, thus bypassing the natural route, and hence the term bypass transition . In the bypass mechanism, elongated high-amplitude disturbances, known as boundary layer streaks, are observed in the pre-transitional region of the flow. Breakdown has been attributed to a secondary instability of these streaks, but the exact dependence has only been speculated and never satisfactorily quantified. The proposed research is first to accurately and efficiently compute the non-linear streaks by using a combined theoretical and numerical approach. We will also analyze the stability of these streaks, and our study will provide an estimate for the required threshold of free-stream disturbances for streak instability. It will also give a quantitative relation between the location where the streaks first become unstable and the intensity of the free-stream disturbances. Such information will be useful for the design of airfoils which operate in transitional flow regimes.