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.

该研究项目的重点是开发和应用严格的分析和计算方法来解决流体动力学和湍流中的一些长期存在的问题，其目标是对平流、平流扩散、纳维-斯托克斯和相关偏微分方程组的解决方案得出物理重要量的可靠数学估计。这些在应用物理科学和工程中具有重要的应用，包括天气预报和气候建模。该项目由三个主要部分组成： 平流：主要研究者和合作者引入的数学混合措施将应用于研究作为层流和湍流混合模型的平流和平流扩散方程的解。分析将对被动示踪剂的混合在搅拌流的体积和/或统计特征方面施加绝对限制，并且它将表明特别有效的搅拌的关键特征。将进行新的最佳搅拌策略的搜索，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问题。经典二维瑞利-贝纳德对流模型中热传输新严格限制的清晰度将通过层流的渐近分析和计算以及湍流的高瑞利数模拟来测试。将利用布辛涅斯​​克近似中温度方程的极大值原理对三维对流进行新的估计。能量耗散和熵产生：将启动一项重要的新计划，以确定有限时间间隔内三维纳维-斯托克斯方程中的最大熵产生。将开发二维纳维-斯托克斯方程中最大回文产生的数学和计算技术。对于当前分析方法失败的简单流动设置，将寻求新方法来确定纳维-斯托克斯方程解中体积和时间平均湍流能量耗散率的绝对极限。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。首席研究员的研究通常涉及与美国及其他地区机构各个不同部门的研究生、博士后、初级教师和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，刺激和激发了新的研究，并促进了数学方法跨学科、机构和国家边界的转移。首席研究员还积极参与有组织的努力，鼓励和加强妇女和代表性不足群体成员参与物理和数学教育和研究。