Mathematical Sciences: Stability of Streak-like Structures in Wall-bounded Shear Flows

9406636 Schmid大量的紊流在近壁面区域显示出条纹状元素的存在。这些连贯的流体模式，特别是它们的持久性和与流动无关的尺度，引起了流体动力学界的极大兴趣和研究。尽管已经发现它们的外观和动力学在向湍流过渡和充分发展的湍流中起着至关重要的作用，但尽管过去几年取得了显著进展，但我们对壁面边界剪切流中的条纹的了解相当有限。本建议旨在通过非线性稳定性分析来研究条纹的动力学及其在湍流运动的产生和维持中的作用。由于实验和计算证据，我们将特别强调条纹状结构击穿的重要阶段。将采用理论和数值相结合的方法，采用Floquet稳定性分析，其中主要的有限振幅扰动状态将由（缓慢衰减的）流向涡组成。三维二次扰动的稳定性方程将在时间和空间框架内使用渐近的、基于特征值的工具和瞬态的、基于初始值的技术进行处理。将进行直接数值模拟，以补充和仔细检查理论结果。本项目的重点将放在流动参数对整体稳定性行为的影响以及对击穿过程动力学的完整描述上。

9406636 Schmid A great number of turbulent fluid flows show the presence of streak-like elements in the near-wall region. These coherent fluid patterns, and in particular their persistence and flow-independent scales, have stimulated a great deal of interest and investigations among the fluid dynamic community. Although it has been found that their appearance and dynamics play a crucial role in the transition to turbulence and in fully developed turbulence, our knowledge about streaks in wall-bounded shear flows is rather limited despite remarkable progress over the past years. The present proposal aims at investigating the dynamics of streaks as well as their role in the production and sustainment of turbulent fluid motion by a nonlinear stability analysis. Owing to experimental and computational evidence, special emphasis will be directed toward the important phase of the breakdown of streak-like structure. A combined theoretical and numerical approach will be taken, employing a Floquet stability analysis where the primary finite-amplitude disturbance state will consist of a (slowly decaying) streamwise vortex. The resulting stability equations for three-dimensional secondary disturbances will then be treated within a temporal and spatial framework using both asymptotic, eigenvalue-based tools and transient, initial-value-based techniques. Direct numerical simulations will be conducted to complement and scrutinize the theoretical results. The emphasis of this project will be on the influence of flow parameters on the overall stability behavior and on the complete description of the dynamics of the breakdown process.