Phase mixing in the fluid mechanics and kinetic theory

流体力学和动力学理论中的相混合

基本信息

  • 批准号:
    1413177
  • 负责人:
  • 金额:
    $ 12.03万
  • 依托单位:
  • 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

项目摘要

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普遍存在的现象,它在理解大气和海洋科学、湍流、天体物理学和受控核聚变的某些方面起着重要作用。例如,它被认为是大气动力学中一个重要的组织机制,有助于解释为什么飓风在很长一段时间内保持其特有的漩涡形状。尽管非线性相混是一种基本的物理机制,但其理论和数学分析仍然难以捉摸。此外,许多这些影响很难在计算或物理实验中分离出来,在这里数学分析可以提供重要的见解。这个项目特别旨在通过研究流体力学和等离子体物理学中各种基本“案例研究”中的效应来扩展我们的数学理解。这个程序的目的是进一步的非线性相位混合的数学分析,通常被认为是困难的,由于高度非正态线性演化和不寻常的规则问题交织在微妙的非线性共振的出现。PI将致力于开发解决这些问题所需的新工具,重点关注四个特定设置:二维Couette流附近不可压缩Navier-Stokes方程(NSE)的消失粘度极限,三维剪切流的非线性不稳定性,二维欧拉中的无粘“旋涡轴对称”和存在外部磁场的Vlasov-Poisson(或Vlasov-Maxwell)中的朗道阻尼。存在许多相关的物理相关问题,可以作为中间步骤或额外的研究方向。在流体力学方面的工作将进一步扩展PI和合作者Nader Masmoudi在最近关于二维Couette流稳定性的工作中所采用的思想[arXiv:1306.5028],特别是使用自适应坐标系和构建用于解释弱非线性共振和非正态瞬态线性行为的规范。在动力学理论方面的工作将进一步发展PI及其合作者Nader Masmoudi和Clement Mouhot在朗道阻尼方面的工作,特别是对等离子体回波的有效处理。最有可能的是,为了扩大动力学理论的应用范围,流体力学工作中的一些思想可能需要适应动力学背景。

项目成果

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Jacob Bedrossian其他文献

Stationary measures for stochastic differential equations with degenerate damping
Pseudo-Gevrey smoothing for the passive scalar equations near Couette
Couette 附近被动标量方程的伪热夫雷平滑
  • DOI:
    10.1016/j.jfa.2025.110987
  • 发表时间:
    2025-10-01
  • 期刊:
  • 影响因子:
    1.600
  • 作者:
    Jacob Bedrossian;Siming He;Sameer Iyer;Fei Wang
  • 通讯作者:
    Fei Wang
Stability Threshold of Nearly-Couette Shear Flows with Navier Boundary Conditions in 2D
  • DOI:
    10.1007/s00220-024-05175-4
  • 发表时间:
    2025-01-11
  • 期刊:
  • 影响因子:
    2.600
  • 作者:
    Jacob Bedrossian;Siming He;Sameer Iyer;Fei Wang
  • 通讯作者:
    Fei Wang
Landau Damping, Collisionless Limit, and Stability Threshold for the Vlasov-Poisson Equation with Nonlinear Fokker-Planck Collisions
  • DOI:
    10.1007/s00220-025-05343-0
  • 发表时间:
    2025-06-04
  • 期刊:
  • 影响因子:
    2.600
  • 作者:
    Jacob Bedrossian;Weiren Zhao;Ruizhao Zi
  • 通讯作者:
    Ruizhao Zi
Existence, Uniqueness and Lipschitz Dependence for Patlak–Keller–Segel and Navier–Stokes in $${\mathbb{R}^2}$$ with Measure-Valued Initial Data

Jacob Bedrossian的其他文献

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{{ truncateString('Jacob Bedrossian', 18)}}的其他基金

Coherent Structure, Chaos, and Turbulence in Fluid Mechanics
流体力学中的相干结构、混沌和湍流
  • 批准号:
    2348453
  • 财政年份:
    2023
  • 资助金额:
    $ 12.03万
  • 项目类别:
    Standard Grant
Conference: CRM Thematic Semester Spring 2022: Probabilities and PDEs
会议:2022 年春季 CRM 主题学期:概率和偏微分方程
  • 批准号:
    2202247
  • 财政年份:
    2022
  • 资助金额:
    $ 12.03万
  • 项目类别:
    Standard Grant
Coherent Structure, Chaos, and Turbulence in Fluid Mechanics
流体力学中的相干结构、混沌和湍流
  • 批准号:
    2108633
  • 财政年份:
    2021
  • 资助金额:
    $ 12.03万
  • 项目类别:
    Standard Grant
CAREER: Inviscid Limits and Stability at High Reynolds Numbers
职业:高雷诺数下的无粘极限和稳定性
  • 批准号:
    1552826
  • 财政年份:
    2016
  • 资助金额:
    $ 12.03万
  • 项目类别:
    Continuing Grant
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:
    1462029
  • 财政年份:
    2014
  • 资助金额:
    $ 12.03万
  • 项目类别:
    Continuing Grant
PostDoctoral Research Fellowship
博士后研究奖学金
  • 批准号:
    1103765
  • 财政年份:
    2011
  • 资助金额:
    $ 12.03万
  • 项目类别:
    Fellowship Award

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RUI:扩展流体系统中主动混合的实验研究
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  • 批准号:
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  • 财政年份:
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