CAREER: Nonlinear stability mechanisms and boundary layer singularities in fluid flows
职业:流体流动中的非线性稳定机制和边界层奇点
基本信息
- 批准号:1911413
- 负责人:
- 金额:$ 35.72万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2018
- 资助国家:美国
- 起止时间:2018-09-01 至 2023-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The project concerns the mathematical analysis of fluid flows in the vicinity of physical boundaries, a fundamental problem in fluid dynamics. The realization that drag forces exerted on a body moving through air (or water) take place on a thin layer around the body lead to the development of boundary layer theory. The practical importance of boundary layer theory in aerodynamics and hydrodynamics is immense: computing the drag on an object and the energy dissipation rate nearby, with implications for fuel efficiency; understanding the problem of wing stall, the dependence of the lift on the angle of attack; and even the enhancement of heat transfer near solid walls. Mathematically, these questions concern the behavior of solutions to the Navier-Stokes equations in the vanishing viscosity limit, and the stability of the ensuing boundary layers. This project will develop new analytical tools to study the validity of the vanishing viscosity limit, the formation of singularities in boundary layers, and to explore the nonlinear stability mechanisms by which these lead to dynamic boundary layer separation. This theoretical information will lead to more accurate reduced models and finer predictions about real fluid flows. The project will train undergraduate, graduate, and post-graduate researchers, in modern research problems in applied mathematics and the tools to study them.This project aims to develop new mathematical tools that will further our understanding of the vanishing viscosity limit: the question whether solutions of the incompressible Navier-Stokes equations converge to solutions of the incompressible Euler equations as the viscosity approaches zero, in the presence of a characteristic physical boundary. For fixed external parameters, the vanishing viscosity limit is equivalent to the infinite Reynolds number limit, and thus this problem is of vital importance to the study of the onset of turbulence in fluid flows. The PI and collaborators will address the emergence of singularities in the Prandtl boundary layer equations by establishing more robust finite time blow-up scenarios. The stability of nearly laminar boundary layers will be studied via a hypocoercive analysis of the Prandtl system and of higher order models. Finally, the PI will develop new energy methods that intertwine Eulerian and Lagrangian approaches to prove the vanishing viscosity limit in high regularity regimes. The goal is to develop nonlinear, solution-adapted methods. Graduate students and post-doctoral fellows will be mentored and included in the research activities.
该项目涉及物理边界附近流体流动的数学分析,这是流体动力学的一个基本问题。对物体在空气(或水)中运动时所施加的阻力发生在物体周围的薄层上的认识,导致了边界层理论的发展。边界层理论在空气动力学和流体动力学中的实际重要性是巨大的:计算物体的阻力和附近的能量耗散率,从而影响燃油效率;了解机翼失速问题,升力对迎角的依赖;甚至是固体壁面附近传热的增强。在数学上,这些问题涉及到Navier-Stokes方程在消失粘度极限下的解的行为,以及随之产生的边界层的稳定性。本项目将开发新的分析工具来研究粘性消失极限的有效性,边界层奇点的形成,并探索这些导致动态边界层分离的非线性稳定性机制。这些理论信息将导致更精确的简化模型和对实际流体流动的更精细的预测。该项目将在应用数学的现代研究问题和研究工具方面培养本科生、研究生和研究生的研究人员。该项目旨在开发新的数学工具,以进一步理解消失的粘度极限:不可压缩的Navier-Stokes方程的解是否收敛于不可压缩的欧拉方程的解,当粘度接近零时,在一个特征物理边界的存在。对于固定的外部参数,粘度消失极限等同于无限雷诺数极限,因此该问题对于研究流体流动中湍流的发生具有重要意义。PI和合作者将通过建立更强大的有限时间爆炸场景来解决普朗特边界层方程中奇点的出现。近层流边界层的稳定性将通过对普朗特系统和高阶模型的准矫顽力分析来研究。最后,PI将开发新的能量方法,将欧拉和拉格朗日方法结合起来,以证明高正则性体系中消失的粘度极限。目标是开发非线性的、解适应的方法。研究生和博士后将接受指导并参与研究活动。
项目成果
期刊论文数量(21)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Weak Solutions of Ideal MHD Which Do Not Conserve Magnetic Helicity
- DOI:10.1007/s40818-020-0076-1
- 发表时间:2020-06-01
- 期刊:
- 影响因子:2.8
- 作者:Beekie, Rajendra;Buckmaster, Tristan;Vicol, Vlad
- 通讯作者:Vicol, Vlad
Convex integration constructions in hydrodynamics
- DOI:10.1090/bull/1713
- 发表时间:2020-11
- 期刊:
- 影响因子:1.3
- 作者:T. Buckmaster;V. Vicol
- 通讯作者:T. Buckmaster;V. Vicol
The Inviscid Limit for the Navier–Stokes Equations with Data Analytic Only Near the Boundary
- DOI:10.1007/s00205-020-01517-3
- 发表时间:2020-04
- 期刊:
- 影响因子:2.5
- 作者:I. Kukavica;V. Vicol;Fei Wang
- 通讯作者:I. Kukavica;V. Vicol;Fei Wang
Remarks on the inviscid limit problem for the Navier-Stokes equations
- DOI:
- 发表时间:2020
- 期刊:
- 影响因子:0
- 作者:I. Kukavica;V. Vicol;Fei Wang
- 通讯作者:I. Kukavica;V. Vicol;Fei Wang
On Moffatt’s Magnetic Relaxation Equations
- DOI:10.1007/s00220-021-04289-3
- 发表时间:2021-04
- 期刊:
- 影响因子:2.4
- 作者:Rajendra Beekie;S. Friedlander;V. Vicol
- 通讯作者:Rajendra Beekie;S. Friedlander;V. Vicol
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
Vlad Vicol其他文献
Vlad Vicol的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
{{ truncateString('Vlad Vicol', 18)}}的其他基金
Collaborative Research: Shock formation, shock development, and the propagation of singularities in fluid dynamics
合作研究:激波形成、激波发展以及流体动力学中奇点的传播
- 批准号:
2307681 - 财政年份:2023
- 资助金额:
$ 35.72万 - 项目类别:
Continuing Grant
CAREER: Nonlinear stability mechanisms and boundary layer singularities in fluid flows
职业:流体流动中的非线性稳定机制和边界层奇点
- 批准号:
1652134 - 财政年份:2017
- 资助金额:
$ 35.72万 - 项目类别:
Continuing Grant
Mathematical Analysis of Fluid Flow at High Reynolds Number from the Point of View of Turbulence
从湍流角度进行高雷诺数流体流动的数学分析
- 批准号:
1514771 - 财政年份:2015
- 资助金额:
$ 35.72万 - 项目类别:
Continuing Grant
Regularity, stability, and singular limits in fluid dynamics
流体动力学的规律性、稳定性和奇异极限
- 批准号:
1348193 - 财政年份:2013
- 资助金额:
$ 35.72万 - 项目类别:
Standard Grant
Regularity, stability, and singular limits in fluid dynamics
流体动力学的规律性、稳定性和奇异极限
- 批准号:
1211828 - 财政年份:2012
- 资助金额:
$ 35.72万 - 项目类别:
Standard Grant
相似海外基金
Stability of standing waves for the nonlinear Schr\"odinger equation with an external potential
具有外势的非线性薛定谔方程的驻波稳定性
- 批准号:
23K03174 - 财政年份:2023
- 资助金额:
$ 35.72万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Stability, Uniqueness, and Existence for Solutions of Hyperbolic Conservation Laws and Nonlinear Wave Equations
双曲守恒定律和非线性波动方程解的稳定性、唯一性和存在性
- 批准号:
2306258 - 财政年份:2023
- 资助金额:
$ 35.72万 - 项目类别:
Standard Grant
DMS-EPSRC Collaborative Research: Stability Analysis for Nonlinear Partial Differential Equations across Multiscale Applications
DMS-EPSRC 协作研究:跨多尺度应用的非线性偏微分方程的稳定性分析
- 批准号:
2219384 - 财政年份:2022
- 资助金额:
$ 35.72万 - 项目类别:
Standard Grant
DMS-EPSRC: Stability Analysis for Nonlinear Partial Differential Equations across Multiscale Applications
DMS-EPSRC:跨多尺度应用的非线性偏微分方程的稳定性分析
- 批准号:
EP/V051121/1 - 财政年份:2022
- 资助金额:
$ 35.72万 - 项目类别:
Research Grant
Stability of Brunn-Minkowski inequalities and Minkowski type problems for nonlinear capacity
Brunn-Minkowski 不等式的稳定性和非线性容量的 Minkowski 型问题
- 批准号:
EP/W001586/1 - 财政年份:2022
- 资助金额:
$ 35.72万 - 项目类别:
Research Grant
Generation mechanism of turbulence coherent structure by three-dimensional flow stability analysis applying nonlinear model
应用非线性模型进行三维流动稳定性分析的湍流相干结构生成机制
- 批准号:
19KK0373 - 财政年份:2022
- 资助金额:
$ 35.72万 - 项目类别:
Fund for the Promotion of Joint International Research (Fostering Joint International Research (A))
DMS-EPSRC Collaborative Research: Stability Analysis for Nonlinear Partial Differential Equations across Multiscale Applications
DMS-EPSRC 协作研究:跨多尺度应用的非线性偏微分方程的稳定性分析
- 批准号:
2219391 - 财政年份:2022
- 资助金额:
$ 35.72万 - 项目类别:
Standard Grant
DMS-EPSRC Collaborative Research: Stability Analysis for Nonlinear Partial Differential Equations across Multiscale Applications
DMS-EPSRC 协作研究:跨多尺度应用的非线性偏微分方程的稳定性分析
- 批准号:
2219397 - 财政年份:2022
- 资助金额:
$ 35.72万 - 项目类别:
Standard Grant
DMS-EPSRC Collaborative Research: Stability Analysis for Nonlinear Partial Differential Equations across Multiscale Applications
DMS-EPSRC 协作研究:跨多尺度应用的非线性偏微分方程的稳定性分析
- 批准号:
2219434 - 财政年份:2022
- 资助金额:
$ 35.72万 - 项目类别:
Standard Grant
Dynamics and Stability of Nonlinear Waves
非线性波的动力学和稳定性
- 批准号:
2204788 - 财政年份:2021
- 资助金额:
$ 35.72万 - 项目类别:
Continuing Grant