Studies in Mathematical Physics: Advection, Convection and Turbulent Transport

数学物理研究：平流、对流和湍流传输

• 批准号: 1205219
• 负责人: Charles Doering
• 金额: $ 52.85万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-08-15 至 2017-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1205219&HistoricalAwards=false
• 关键词: Studies; Mathematical; Physics; Advection; Convection

This research program is focused on the development and application of rigorous analytical and computational approaches to some longstanding problems in fluid dynamics and turbulence with the goal of deriving reliable mathematical estimates of physically important quantities for solutions of the advection, advection-diffusion, and Navier-Stokes and related systems of partial differential equations. These have important applications in the applied physical sciences and engineering, including weather prediction and climate modeling. The project has three major components: Advection: Mathematical mixing measures introduced by the principal investigator and collaborators will be applied to study solutions of the advection and advection-diffusion equations as models of laminar and turbulent mixing. Analysis will place absolute limits on mixing for passive tracers in terms of bulk and/or statistical features of the stirring flows, and it will indicate key features of particularly efficient stirring. New searches for optimal stirring strategies will be undertaken, and the mixing effectiveness of turbulence will be investigated. Convection: Issues in thermal convection will be studied via analysis and direct numerical simulation. The sharpness of new rigorous limits on heat transport in the classical two-dimensional model of Rayleigh-Benard convection will be tested via asymptotic analysis and computation of laminar flows and high Rayleigh number simulations of turbulent flows. New estimates for three-dimensional convection will be pursued exploiting the maximum principle for the temperature equation in the Boussinesq approximation. Energy dissipation and enstrophy production: A major new program to determine maximal enstrophy production in the three-dimensional Navier-Stokes equations over finite time intervals will be initiated. Mathematical and computational techniques in the context of maximal palinstrophy production in the two dimensional Navier-Stokes equations will be developed. New methods for determining absolute limits on the bulk and time averaged turbulent energy dissipation rate in solutions of the Navier-Stokes equations will be sought for simple flow setups where current analysis methods fail. Broader impacts: These projects are suitable for doctoral students and postdoctoral researchers at the University of Michigan. The Principal Investigator's research routinely involves collaborations with graduate students, postdocs, junior faculty, and distinguished senior researchers in a variety of different departments at institutions across the United States and beyond. These interactions foster broad dissemination of results, stimulate and motivate new investigations, and promote transfer of mathematical methods across disciplinary, institutional, and national boundaries. The Principal Investigator is also actively engaged in organized efforts to encourage and enhance the participation of women and members of under-represented groups in physics and mathematics education and research.

该研究计划的重点是针对流体动力学和湍流的一些长期问题的严格分析和计算方法的开发和应用，目的是在物理上重要的数学量来得出对流，对流 - 扩散以及偏微分方程的Navier-Stokes和Navier-Stokes和相关系统的可靠数学估计。这些在应用的物理科学和工程中具有重要的应用，包括天气预测和气候建模。该项目具有三个主要组成部分：对流：主要研究者和合作者引入的数学混合度量，将应用于对流和对流扩散方程的解决方案，作为层状和湍流混合模型。分析将在搅拌流的批量和/或统计特征方面对被动示踪剂混合的绝对限制，这将表明特别有效搅拌的关键特征。将进行最佳搅拌策略的新搜索，并将研究湍流的混合有效性。对流：将通过分析和直接数值模拟来研究热对流的问题。在雷利 - 贝纳德对流的经典二维模型中，新的严格限制对热传输的清晰度将通过渐近分析和层流流的计算以及湍流的高瑞利数量模拟进行测试。将追求三维对流的新估计值，以利用BousSinesQ近似中温度方程的最大原理。能量耗散和肠病生产：将在有限的时间间隔内确定三维Navier-Stokes方程中最大的腹膜生产的主要新计划。将开发在最大的壁画产生中，将开发在两个维纳维尔 - 斯托克斯方程中的数学和计算技术。对于当前分析方法失败的简单流程设置，将寻求确定整体上的绝对限制和时间平均的湍流能量耗散速率的新方法。更广泛的影响：这些项目适合密歇根大学的博士生和博士后研究人员。首席研究人员的研究通常涉及与研究生，博士后，初级教师以及美国及其他机构各个不同部门的杰出高级研究人员的合作。这些相互作用促进了结果的广泛传播，刺激和激励新的研究，并促进数学方法在纪律，制度和民族边界之间的转移。首席研究者还积极从事有组织的努力，以鼓励和增强妇女和代表性不足的团体的参与物理学和数学教育和研究。