Instability of Fluid Flows
流体流动的不稳定性
基本信息
- 批准号:0604050
- 负责人:
- 金额:$ 9.49万
- 依托单位:
- 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:2006-06-01 至 2009-05-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Shvydkoy0604050 Instability of fluid motion is the main subject of thisproposal. Although it was a classical and rather experimentalbranch of the hydrodynamics in the early days, it now stands asan actively developing area of modern analytical fluid dynamics,and it provides many challenging problems to mathematicians. Themotion of an ideal incompressible fluid is governed by the Eulerequation. Because of the particular structure of the nonlinearitypresent in the equation it appears to be notoriously difficult toanswer even the most basic questions in a rigorous mathematicalway. One of these questions is to justify the Lyapunovlinearization method for stationary fluid flows. In particular,if the Euler equation linearized about a given equilibrium hasunstable spectrum, does this imply that the equilibrium isunstable in the nonlinear sense, say, in the basic energy norm?The investigator studies this and other questions related toinstability and spectra. These include: the question of findingunstable shortwave perturbations for general fluid flows;analysis of the spectrum for the Euler equations and therelationship with the spectrum of weakly viscous flows in thelimit of vanishing viscosity. The investigator examines theseproblems using modern WKB-type asymptotic analysis for the Eulerequations, pseudo-differential calculus, as well as newlydeveloped connections between the cocycle theory and fluiddynamics. The questions addressed in this particular project areclosely related to the fundamental problems of environmentalscience such as weather prediction, climate change, and oceanicmotion. Instability of large fluid masses is inherent in thenature of those processes, while large scale instabilities oftengrow out of small scales. The investigator presents mechanismsfor such small scale instabilities and gives them a precisemathematical description. Understanding instabilities in fluidflows is important for a broad range of questions in atmosphericscience and geophysics.
Shvydkoy0604050 流体运动的不稳定性是本提案的主要主题。尽管它在早期是流体力学的一个经典的、相当实验性的分支,但现在它已成为现代分析流体动力学的一个活跃发展的领域,它为数学家提供了许多具有挑战性的问题。理想不可压缩流体的运动由欧拉方程控制。由于方程中存在的非线性的特殊结构,以严格的数学方式回答最基本的问题似乎是出了名的困难。这些问题之一是证明静态流体流动的李亚普诺夫线性化方法的合理性。特别是,如果关于给定平衡线性化的欧拉方程具有不稳定谱,这是否意味着平衡在非线性意义上(例如基本能量范数)不稳定?研究者研究这个问题以及与不稳定性和谱相关的其他问题。其中包括:寻找一般流体流动的不稳定短波扰动问题;欧拉方程谱的分析以及在消失粘度极限下与弱粘性流谱的关系。研究人员使用现代 WKB 型欧拉方程渐近分析、伪微分演算以及新开发的余循环理论和流体动力学之间的联系来研究这些问题。 这个特定项目解决的问题与天气预报、气候变化和海洋运动等环境科学的基本问题密切相关。大流体质量的不稳定性是这些过程的本质所固有的,而大规模的不稳定性往往是从小规模中产生的。研究人员提出了这种小规模不稳定性的机制,并给出了精确的数学描述。了解流体流动的不稳定性对于大气科学和地球物理学中的广泛问题非常重要。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Roman Shvydkoy其他文献
The Essential Spectrum of Advective Equations
- DOI:
10.1007/s00220-006-1537-4 - 发表时间:
2006-02-28 - 期刊:
- 影响因子:2.600
- 作者:
Roman Shvydkoy - 通讯作者:
Roman Shvydkoy
Well-posedness and Long Time Behavior of the Euler Alignment System with Adaptive Communication Strength
具有自适应通信强度的欧拉对准系统的适定性和长时间行为
- DOI:
- 发表时间:
2023 - 期刊:
- 影响因子:0
- 作者:
Roman Shvydkoy;Trevor Teolis - 通讯作者:
Trevor Teolis
Generic alignment conjecture for systems of Cucker–Smale type
Cucker-Smale 型系统的一般对齐猜想
- DOI:
- 发表时间:
2024 - 期刊:
- 影响因子:0
- 作者:
Roman Shvydkoy - 通讯作者:
Roman Shvydkoy
Roman Shvydkoy的其他文献
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{{ truncateString('Roman Shvydkoy', 18)}}的其他基金
Hydrodynamics of Collective Phenomena and Applications
集体现象的流体动力学及其应用
- 批准号:
2107956 - 财政年份:2021
- 资助金额:
$ 9.49万 - 项目类别:
Standard Grant
Mathematics of Collective Behavior: From Self-Organized Dynamics to Fluid Turbulence
集体行为数学:从自组织动力学到流体湍流
- 批准号:
1813351 - 财政年份:2018
- 资助金额:
$ 9.49万 - 项目类别:
Standard Grant
Mechanisms for Energy Conservation in Onsager Supercritical Fluids
Onsager 超临界流体的节能机制
- 批准号:
1515705 - 财政年份:2015
- 资助金额:
$ 9.49万 - 项目类别:
Continuing Grant
Anomalous dissipation in fluids, deterministic turbulence, and intermittency
流体中的反常耗散、确定性湍流和间歇性
- 批准号:
1210896 - 财政年份:2012
- 资助金额:
$ 9.49万 - 项目类别:
Standard Grant
Onsager's conjecture and the energy of singular flows
昂萨格猜想和奇异流能量
- 批准号:
0907812 - 财政年份:2009
- 资助金额:
$ 9.49万 - 项目类别:
Continuing Grant
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