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
• 负责人: Michael Jolly
• 金额: $ 2.16万
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-07-01 至 2014-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1008861&HistoricalAwards=false
• 关键词: Collaborative; Research; Analysis; incompressible; Reynolds

The purpose of this project is to conduct international collaborative research, between two teams of scientists from the USA and Brazil, in the mathematical analysis and modeling of turbulent incompressible fluids. The topics to be investigated are: small viscosity regime of second grade fluids; uniqueness of weak solutions for certain linear perturbations of the two-dimensional Euler equations; the vanishing viscosity limit of the three-dimensional Navier-Stokes equations with helical symmetry; the search for hypotheses on the structure of invariant measures or stationary statistical solutions of the two and three-dimensional Navier-Stokes equations with anomalous dissipation; the search for energy cascade for flows in domains with physical boundaries; two-dimensional cascades with large gap bimodal forcing. Turbulence is a common phenomenon in fluid motion, in which macroscopic quantities (velocity, pressure, temperatures, etc.) no longer have a deterministic relation with global parameters of the flow. Direct numerical simulations of turbulent flows at large Reynolds numbers, that occur in practical applications, such as in geophysical modeling and mixing in industrial processes, are out of reach even for the state-of-the-art computer power. Therefore, there is an urgent need to pursue this challenging problem analytically, by developing rigorous mathematical and statistical tools to investigate it, and to test these tools computationally. While turbulence is an everyday occurrence, our understanding is still lacking in many aspects. Quantifying the effect of small scales on the dynamics of large scales is fundamental in modern multiscale science. The goal of the project is to enable a predictive analytical study of turbulent flows. This study will impact wide-ranging applications, from geophysical modeling, such as dispersion of pollutants in the ocean, to biological and industrial modeling, such as design of polymeric materials. The project will consolidate the well-established collaborative efforts of the principal investigators with their Brazilian counterparts, and may lead to new collaboration, especially among the junior research personnel. International collaboration among scientists is a key to economic competitiveness in global markets. Four US and three Brazilian academic institutions are involved in the project. The international dimension of the project is further emphasized through two planned workshops. Training and supervision of at least six Ph.D. students and postdoctoral fellows is also achieved through planned summer schools and scientific workshops. Students and postdoctoral fellows from the US will travel to Brazil to participate in the workshops and the summer schools and interact with the US and Brazilian researchers.This project is co-funded with the Americas Program of the Office of International Science and Engineering.

该项目的目的是在来自美国和巴西的两个科学家团队之间进行国际合作研究，对湍流不可压缩流体进行数学分析和建模。研究课题为：二级流体的小粘度状态；二维欧拉方程的某些线性扰动的弱解的唯一性；具有螺旋对称性的三维纳维-斯托克斯方程的消失粘度极限；寻找关于具有反常耗散的二维和三维纳维-斯托克斯方程的不变测度或平稳统计解的结构的假设；寻找具有物理边界的域中流动的能量级联；具有大间隙双峰强迫的二维级联。湍流是流体运动中的一种常见现象，其中宏观量（速度、压力、温度等）不再与流动的全局参数具有确定性关系。即使对于最先进的计算机能力来说，在实际应用中（例如地球物理建模和工业过程中的混合）中发生的大雷诺数湍流的直接数值模拟也是遥不可及的。因此，迫切需要通过开发严格的数学和统计工具来研究这个具有挑战性的问题，并通过计算测试这些工具。虽然湍流每天都会发生，但我们在许多方面仍然缺乏了解。量化小尺度对大尺度动力学的影响是现代多尺度科学的基础。该项目的目标是实现湍流的预测分析研究。这项研究将影响广泛的应用，从地球物理建模（例如海洋污染物的扩散）到生物和工业建模（例如聚合物材料的设计）。该项目将巩固主要研究人员与巴西同行的良好合作成果，并可能带来新的合作，特别是初级研究人员之间的合作。科学家之间的国际合作是全球市场经济竞争力的关键。四家美国和三家巴西学术机构参与了该项目。通过计划举办的两次研讨会进一步强调了该项目的国际影响力。至少六名博士的培训和监督学生和博士后研究员也是通过计划的暑期学校和科学讲习班来实现的。来自美国的学生和博士后将前往巴西参加研讨会和暑期学校，并与美国和巴西的研究人员互动。该项目与国际科学与工程办公室美洲项目共同资助。