Phase mixing in the fluid mechanics and kinetic theory

流体力学和动力学理论中的相混合

• 批准号: 1413177
• 负责人: Jacob Bedrossian
• 金额: $ 12.03万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-06-15 至 2014-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1413177&HistoricalAwards=false
• 关键词: Phase; mixing; fluid; mechanics; kinetic

Nonlinear mixing is a ubiquitous behavior observed in fluids and plasmas which plays an important role in understanding certain aspects of atmosphere and ocean sciences, turbulence, astrophysics and controlled fusion. For example, it is thought to be an important organizing mechanism in atmospheric dynamics that helps to explain why hurricanes retain their characteristic vortex shape for extended periods of time. Despite being a fundamental physical mechanism, the theoretical and mathematical analysis of nonlinear phase mixing has remained elusive. Moreover, many of these effects are difficult to isolate in computational or physical experiments and here mathematical analysis can provide important insights. This project specifically aims to expand our mathematical understanding by studying the effect in a variety of fundamental 'case studies' found in fluid mechanics and plasma physics.The purpose of this program is to further the mathematical analysis of nonlinear phase mixing, generally regarded as difficult due to the appearance of highly non-normal linear evolutions and unusual regularity issues intertwined with subtle nonlinear resonances. The PI will work to develop new tools necessary to approach these problems with a focus on working towards four specific settings: the vanishing viscosity limit of the incompressible Navier-Stokes equations (NSE) near the 2D Couette flow, the nonlinear instability of 3D shear flows, inviscid 'vortex axisymmetrization' in 2D Euler and Landau damping in Vlasov-Poisson (or Vlasov-Maxwell) in presence of external magnetic fields. Many related physically relevant problems exist, and may serve as intermediate steps or additional lines of research. The work in fluid mechanics will expand further on ideas employed by the PI and collaborator Nader Masmoudi in the recent work on the stability of 2D Couette flow [arXiv:1306.5028], especially the use of adaptive coordinate systems and the construction of norms which account for weakly nonlinear resonances and the non-normal transient linear behavior. The work in kinetic theory will further develop techniques used in the work of the PI and collaborators Nader Masmoudi and Clement Mouhot on Landau damping [arXiv:1311.2870], especially the efficient treatment of the plasma echoes. Most likely, in order to expand the range of kinetic theory applications, some ideas from the work in fluid mechanics may need to be adapted to the kinetic setting.

非线性混合是在流体和等离子体中观察到的一种无处不在的行为，它在理解大气和海洋科学的某些方面，湍流，天体物理学和受控融合方面起着重要作用。例如，它被认为是大气动力学中的重要组织机制，有助于解释为什么飓风在长时间内保留其特征性的涡旋形状。尽管是基本的物理机制，但非线性相混合的理论和数学分析仍然难以捉摸。此外，这些效果中的许多很难在计算或物理实验中分离，在这里数学分析可以提供重要的见解。该项目特别旨在通过研究在流体力学和等离子体物理学中发现的各种基本“案例研究”中的效果来扩展我们的数学理解。该程序的目的是进一步对非线性相混合的数学分析，通常由于高度非正常的线性演化的出现而被认为是困难的，因此很难与非线性的规律性相互互动，而不是属于非线性的不合理性。 The PI will work to develop new tools necessary to approach these problems with a focus on working towards four specific settings: the vanishing viscosity limit of the incompressible Navier-Stokes equations (NSE) near the 2D Couette flow, the nonlinear instability of 3D shear flows, inviscid 'vortex axisymmetrization' in 2D Euler and Landau damping in Vlasov-Poisson (or Vlasov-Maxwell)在外部磁场的情况下。存在许多相关的物理相关问题，并且可以用作中间步骤或其他研究线。流体力学中的工作将进一步扩展到PI和合作者Nader Masmoudi在最近关于2D COUETTE FLOW的稳定性[ARXIV：1306.5028]的稳定性中所采用的想法，尤其是使用适应性坐标系统，尤其是使用规范的构建，这些规范构建了弱的非线性共鸣和非正态的固定性固定持续性固定行为。动力学理论的工作将进一步开发用于PI和合作者Nader Masmoudi和Clement Mouhot在Landau Damping [Arxiv：1311.2870]中使用的技术，尤其是对等离子体回声的有效处理。为了扩大动力学理论应用的范围，最有可能的是流体力学中的某些想法可能需要适应动力学环境。