A study of how indicators for 2-D turbulence depend on the driving force in the Navier-Stokes equation

研究二维湍流指标如何取决于纳维-斯托克斯方程中的驱动力

基本信息

  • 批准号:
    0511533
  • 负责人:
  • 金额:
    $ 28.36万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2005
  • 资助国家:
    美国
  • 起止时间:
    2005-06-01 至 2010-05-31
  • 项目状态:
    已结题

项目摘要

This project is focused on the discovery of driving forces that supportthe Kraichnan theory of 2-D fully developed turbulence. In recent workthe investigators and their collaborators have identified critical wavenumbers expressed as averages of different norms of the solution to theNavier-Stokes equations (NSE). These wave numbers provide necessary, andnearly sufficient conditions for the Kraichnan theory to hold. This teamhas also localized to some extent the global attractor of the NSE in aplane spanned by two of these norms (one being the energy), to helpunderstand which driving forces produce these conditions. The proposedwork will combine this analysis with computational optimization to zero inon such forces, and then study in detail the turbulent features theyproduce. The mathematical treatment of turbulence is largely driven bythe heuristic theories of Kolmogorov, Batchelor and Kraichnan. Theapproach taken in projecting the attractor however, seems to be entirelynew. The information provided by this analysis will guide thecomputational component which otherwise would be confronted with a vastlandscape of possible driving forces to consider.Turbulence is readily observed in three-dimensional physical spacedomains. Most people think of a bumpy plane rides (in this case thedomain is the volume around the airplane). Like the swirls generated byrocks in a stream, rapidly changing patterns form in the air around theplane. Turbulence theories do not attempt to predict the precisedevelopment of these patterns, but rather find (a) consistent laws whichdescribe how, on average, energy is transferred to smaller length scales,and (b) critical length scales at which this this phenomenon changes. True 2-D flows in nature are less prevalent. The most prominent example,the earth's atmosphere, is actually a thin 3-D domain, whose behaviorapproaches that of a 2-D flow. The fate of energy over different lengthscales is more complicated for 2-D flow, though that of 3-D flow is insome sense embedded into it. Though 2-D experiments are difficult tocarry out in the laboratory, they allow for much finer study on acomputer. Of all 2-D flows, the one studied in this project is arguablythe most amenable to analysis and efficient simulation. Yet it isfundamental, not only to 2-D and nearly 2-D flows such as the atmosphere,but also to 3-D turbulence due to universality.
这个项目的重点是发现支持Kraichnan二维完全发展湍流理论的驱动力。在最近的工作中,研究人员和他们的合作者已经确定了用navier - stokes方程(NSE)解的不同范数的平均值表示的临界波数。这些波数为克雷契南理论的成立提供了必要的和几乎充分的条件。该团队还在一定程度上将NSE的全局吸引子定位在由两个规范(一个是能量)跨越的平面上,以帮助理解是哪些驱动力产生了这些条件。所提出的工作将把这种分析与计算优化结合起来,以消除这种力,然后详细研究它们产生的湍流特征。湍流的数学处理在很大程度上是由Kolmogorov、Batchelor和Kraichnan的启发式理论推动的。然而,投射吸引子的方法似乎是全新的。该分析提供的信息将指导计算组件,否则将面临大量可能的驱动力。湍流很容易在三维物理空间中观察到。大多数人想到的是颠簸的飞机(在这种情况下,域是飞机周围的体积)。就像溪流中岩石形成的漩涡一样,飞机周围的空气中也形成了快速变化的图案。湍流理论并不试图预测这些模式的精确发展,而是找到(a)描述能量平均如何转移到较小长度尺度的一致定律,以及(b)这种现象发生变化的临界长度尺度。真正的二维流动在自然界中不那么普遍。最突出的例子是地球大气层,它实际上是一个薄的3-D域,其行为接近于2-D流。能量在不同长度尺度上的命运对于二维流动来说更为复杂,尽管三维流动在某种意义上嵌入其中。虽然二维实验很难在实验室中进行,但它们允许在计算机上进行更精细的研究。在所有二维流中,本项目研究的二维流可以说是最易于分析和有效模拟的。然而,它不仅是二维和接近二维的流动(如大气)的基础,而且由于其普遍性,它也是三维湍流的基础。

项目成果

期刊论文数量(0)
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Michael Jolly其他文献

Improving Sglt2i Use On Our Interventional Cardiology Service For Patients At Risk For Heart Failure
  • DOI:
    10.1016/j.cardfail.2023.10.457
  • 发表时间:
    2024-01-01
  • 期刊:
  • 影响因子:
  • 作者:
    Aditya Kesari;Katherine Crawford;Joseph Campbell;Christopher Huff;Michael Jolly
  • 通讯作者:
    Michael Jolly
LOST IN THE CLOTS: A CASE OF PRIMARY PULMONARY ARTERY SARCOMA MASQUERADING AS A PULMONARY EMBOLISM
  • DOI:
    10.1016/s0735-1097(24)04772-7
  • 发表时间:
    2024-04-02
  • 期刊:
  • 影响因子:
  • 作者:
    Sarah Grebennikov;Michael Jolly;Joseph Campbell;Mitchell J. Silver
  • 通讯作者:
    Mitchell J. Silver
Outcomes of Endovascular Venous Stenting in Patients Receiving Direct Oral Anticoagulants and Antiplatelet Therapy: A Single-Center Experience
  • DOI:
    10.1016/j.jvsv.2019.12.039
  • 发表时间:
    2020-03-01
  • 期刊:
  • 影响因子:
  • 作者:
    Katherine Hays;Michael Jolly;Raghu Kolluri
  • 通讯作者:
    Raghu Kolluri
Red Flags for IPO Downfalls in New Zealand
新西兰IPO失败的危险信号
  • DOI:
    10.1108/mf-05-2017-0197
  • 发表时间:
    2017
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Huong Dang;Michael Jolly
  • 通讯作者:
    Michael Jolly
Linear morphea masquerading as superficial thrombophlebitis
伪装成血栓性浅静脉炎的线状硬斑病
  • DOI:
  • 发表时间:
    2018
  • 期刊:
  • 影响因子:
    3.5
  • 作者:
    Michael Jolly;Seth Bendo;R. Kolluri
  • 通讯作者:
    R. Kolluri

Michael Jolly的其他文献

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{{ truncateString('Michael Jolly', 18)}}的其他基金

A Computational Study of the Nudging Approach to Data Assimilation
数据同化助推方法的计算研究
  • 批准号:
    1818754
  • 财政年份:
    2018
  • 资助金额:
    $ 28.36万
  • 项目类别:
    Continuing Grant
Collaborative Research: Determining Forms and Data Assimilation with Stochastic Data
协作研究:利用随机数据确定形式和数据同化
  • 批准号:
    1418911
  • 财政年份:
    2014
  • 资助金额:
    $ 28.36万
  • 项目类别:
    Standard Grant
Collaborative Proposal: Study of turbulence in physical systems through complex singularities and determining modes
合作提案:通过复杂奇点和确定模式研究物理系统中的湍流
  • 批准号:
    1109638
  • 财政年份:
    2011
  • 资助金额:
    $ 28.36万
  • 项目类别:
    Standard Grant
Collaborative Research: Analysis of incompressible high Reynolds number flows
合作研究:不可压缩高雷诺数流动分析
  • 批准号:
    1008861
  • 财政年份:
    2010
  • 资助金额:
    $ 28.36万
  • 项目类别:
    Standard Grant
FRG Collaborative Research: Approximation of Lyapunov exponents
FRG 协作研究:Lyapunov 指数的近似
  • 批准号:
    0139874
  • 财政年份:
    2002
  • 资助金额:
    $ 28.36万
  • 项目类别:
    Standard Grant
Approximation of the Global Attractors of Evolution Equations
进化方程全局吸引子的近似
  • 批准号:
    0074460
  • 财政年份:
    2000
  • 资助金额:
    $ 28.36万
  • 项目类别:
    Standard Grant
Approximation of the Global Attractors of Evolution Equations
进化方程全局吸引子的近似
  • 批准号:
    9706903
  • 财政年份:
    1997
  • 资助金额:
    $ 28.36万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Approximation of the Global Attractors of Evolution Equations
数学科学:进化方程全局吸引子的近似
  • 批准号:
    9404340
  • 财政年份:
    1994
  • 资助金额:
    $ 28.36万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Approximation of the Global Attractors of Evolution Equations
数学科学:进化方程全局吸引子的近似
  • 批准号:
    9007802
  • 财政年份:
    1990
  • 资助金额:
    $ 28.36万
  • 项目类别:
    Continuing Grant

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