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

数学科学：壁面剪切流中条纹状结构的稳定性

• 批准号: 9406636
• 负责人: Peter Schmid
• 金额: $ 6万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-15 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9406636&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Stability; Streak; like

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.

小行星9406636 大量的湍流流动表明近壁区存在条纹状单元。这些连贯的流体模式，特别是他们的持久性和流动无关的规模，激发了大量的兴趣和研究之间的流体动力学社区。 虽然人们已经发现，它们的外观和动力学起着至关重要的作用，在过渡到湍流和充分发展的湍流，我们的知识条纹在壁边界剪切流是相当有限的，尽管在过去的几年中取得了显着的进展。本建议的目的是调查条纹的动力学，以及它们的作用，在生产和维持湍流运动的非线性稳定性分析。 由于实验和计算的证据，特别强调将针对条纹状结构的崩溃的重要阶段。 将采取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包括（缓慢衰减的）流向涡。所得的三维二次扰动的稳定性方程，然后将在时间和空间的框架内使用渐近，基于特征值的工具和瞬态，基于初始值的技术进行处理。直接数值模拟将进行补充和审查的理论结果。该项目的重点将是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。