Streak Instability and Bypass Transition

层流-湍流转捩是流体力学中的一个基本问题，对预测阻力、气动加热和流动分离具有重要意义。例如，过渡到湍流可以绕过压气机中的流动分离，在低压涡轮级，50%的流动可以过渡。虽然最终状态可能总是一个平衡的湍流边界层，但过渡本身可以由不同的机制介导，每种机制导致明显不同的过渡位置和长度。文献一般将过渡情景分为自然或有序的途径和旁路机制。前者的特征是粘性的T-S不稳定波，在安静的测试条件下可以观察到。在存在自由流扰动的情况下，这种扰动被粗略地称为自由流湍流（FST），转换发生得更快，从而绕过自然路线，因此称为旁路转换。在旁路机制中，在流动的过渡前区域观察到细长的高振幅扰动，称为边界层条纹。击穿归因于这些条纹的二次不稳定性，但确切的依赖关系只是推测，从未令人满意地量化。本研究首次采用理论与数值相结合的方法对非线性条纹进行了精确、高效的计算。我们还将分析这些条纹的稳定性，我们的研究将提供对条纹不稳定性所需的自由流扰动阈值的估计。它还将给出条纹首先变得不稳定的位置与自由流扰动强度之间的定量关系。这样的信息将是有用的设计在过渡流动制度的翼型。

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.