Qualitative Behavior of Turbulent Flows

湍流的定性行为

• 批准号: 0604886
• 负责人: Igor Kukavica
• 金额: --
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-06-15 至 2010-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0604886&HistoricalAwards=false
• 关键词: Qualitative; Behavior; Turbulent; Flows

Kukavica0604886 This project is concerned with solutions of theNavier-Stokes equations, which are the principal model for flowof a viscous incompressible fluid. The investigator addressesquestions regarding regularity, qualitative behavior of solutions(size, complexity, decay), qualitative description of attractors,determination of solutions by observables, and minimal scale. Similar questions are addressed for the Euler equations,Kuramoto-Sivashinsky equation, and the complex Ginzburg-Landauequation. The understanding of dynamics of a fluid flow is importantin many applied fields, such as oceanography, atmosphericscience, aerodynamics, and turbulence theory. The Navier-Stokesequations are the main model for study of the viscous fluid flow. The equations have a rich history and have been a subject ofintense study due to their immense challenges and their directconnections with applications. The investigator studiesregularity questions and qualitative behavior of solutions. Potential applications include better understanding of smallstructures of turbulent flows (vortices, oscillations),reconstructing dynamics from measurements, and a rigorousinterpretation of numerical simulations of a fluid motion.

这个项目涉及的是粘性不可压缩流体流动的主要模型navier - stokes方程的解。研究者解决了关于规律性、溶液的定性行为（大小、复杂性、衰减）、吸引子的定性描述、通过可观察物和最小尺度确定溶液的问题。对于欧拉方程、Kuramoto-Sivashinsky方程和复杂的Ginzburg-Landauequation，也提出了类似的问题。对流体流动动力学的理解在许多应用领域都很重要，如海洋学、大气科学、空气动力学和湍流理论。navier - stokes方程组是研究粘性流体流动的主要模型。这些方程有着丰富的历史，由于其巨大的挑战和与应用的直接联系，一直是一个密切研究的主题。研究者研究规律性问题和解的定性行为。潜在的应用包括更好地理解湍流的小结构（漩涡，振荡），从测量中重建动力学，以及对流体运动的数值模拟的严格解释。