Mathematical Fluid Dynamics and Education Turbulent Transport, Combustion, and Compressible Convection

小行星9701942 这项工作得到了美国国家科学基金会的支持， 职业发展奖。 研究部分将侧重于 对流体现象的理论理解。具体来说，这些研究 的努力概述了湍流输送和标量不透明度的研究， 预混燃烧中增强燃烧速度的数值计算， 弱可压缩输运的理论和计算研究 现象。这项工作的一个基本主题是， 流动特性影响运输现象，其中可能包括增强 混合率，增强的罕见事件概率，增强的燃烧速度，以及 增强的滞弹性热传递。这些研究涉及一个复杂的 现代渐近，数值和概率技术的集成。 此外，该奖项将支持持续的课程开发 高级本科/研究生水平的数学流体动力学 当然了 这样的课程旨在向学生提供基本的 理解流体力学所必需的数学工具， 使学生掌握解决研究问题的基本技术 应用数学 此外，一个小的演示流体 将开发一个实验室，提供许多流体的可视化 现象。 这个教师早期职业发展奖将提供主要的 调查员有机会继续他的研究工作， 了解许多流体输送现象，同时 开发新的教育课程。发展流体的合理理论 运输在许多方面都是至关重要的。 实验理解 流体湍流通常涉及被动染料的跟踪，并且， 因此，流体流动特性如何影响 这种染料的混合是关键的。 此外，发展健全的交通 理论自然会产生对各种混合应用的洞察力 例如追踪大气污染物。 也许最重要的是 这些理论可能提供的大规模潜在信息 计算流体，燃烧和气候模型，其中一个共同的 困难在于如何处理不可分辨的长度和时间尺度。 这是一 在计算流体力学中，存在着一个公认的事实，即重要的、不可忽略的、复杂的流体现象，而这些现象是根本无法解决的 即使是最大的超级计算机。 这些次网格效应对我们的生活 在许多流体应用中发挥重要作用，例如天气预报。它们不能被 被忽略了，标准的方法是用更简单的东西来代替它们-- 有效混合系数。 在许多应用中，输运理论 在这里开发提供健全的理由和量化这些 系数，并可能提供现有的改进， 计算模型 最后，课程工作将涉及 开发一个小型流体实验室，包括一个示范水 隧道 通过这个实验，学习流体理论的学生会发现 与真实的流体现象的令人兴奋的视觉接触， 数学课程，这种可视化将导致更大的 兴奋和赞赏数学理论的有用性， 理解可观察到的现象。 美国国家科学基金会强烈鼓励早期 发展学术教师作为教育工作者和研究人员。 的 教师早期职业发展（CAREER）计划是一个基金会范围内的计划，为初级教师提供支持， 在整体职业发展的背景下。 它结合在一个单一的 计划在最广泛的意义上支持高质量的研究和教育 以及传统上在科学领域代表性不足的人的充分参与 与工程学 该计划增强并强调了 基金会致力于发展全面、均衡的学术 包括研究和教育的职业。

9701942 McLaughlin This work is supported by a National Science Foundation Faculty Early Career Development Award. The research component will focus on the theoretical understanding of fluid phenomena. Specifically, these research efforts outline the study of turbulent transport and scalar intermittency, the numerical calculation of enhanced burning speeds in premixed combustion, and theoretical and computational studies of weakly compressible transport phenomena. An underlying theme in this effort is the isolation of how fluid flow properties affect transport phenomena, which may include enhanced mixing rates, enhanced rare event probability, enhanced burning speeds, and enhanced anelastic heat transport. These studies involve a sophisticated integration of modern asymptotic, numerical, and probabilistic techniques. Additionally, this award will support the continued curriculum development of an advanced undergraduate/ graduate level Mathematical Fluid Dynamics course. Such a course is designed to present the student with the essential mathematical tools necessary to understand fluid mechanics and to quickly equip the student with essential techniques for attacking research problems in Applied Mathematics. Additionally, a small demonstration fluids laboratory will be developed to offer visualization of many fluid phenomena. This Faculty Early Career Development Award will provide the principal investigator the opportunity to pursue his research efforts in the understanding of many fluid transport phenomena while additionally developing new educational curricula. Developing sound theories for fluid transport is fundamental in many ways. The experimental understanding of fluid turbulence typically involves the tracking of passive dye, and, consequently, the quantification of how fluid flow properties affect the mixing of such dye is critical. Further, the development of sound transport theories naturally will yield insight into a va riety of mixing applications such as the tracking of atmospheric pollutants. Perhaps most importantly is the potential information such theories may offer to large-scale computational fluids, combustion and climate models in which a common difficulty regards how to treat unresolvable length and time scales. It is an accepted fact in computational fluid dynamics that important, non- negligible, complex fluid phenomena exist which are simply not resolvable on even the largest supercomputers. These sub-grid effects play a dramatic role in many fluids applications such as weather prediction. They cannot be ignored, and a standard approach is to replace them by something simpler-- an effective mixing coefficient. In many applications, the transport theories developed here offer sound justification and quantification of these coefficients, and potentially may offer improvements to existing computational models. Finally, the curriculum effort will involve the development of a small fluids laboratory including a demonstration water tunnel. Through this lab, a student studying the theory of fluids will find exciting visual contact with real fluids phenomena typically unavailable in mathematics coursework, and this visualization will lead to greater excitement and appreciation for the usefulness of mathematical theory in the understanding of observable phenomena. The National Science Foundation strongly encourages the early development of academic faculty as both educators and researchers. The Faculty Early Career Development (CAREER) Program is a Foundation- wide program that provides for the support of junior faculty within the context of their overall career development. It combines in a single program the support of quality research and education in the broadest sense and the full participation of those traditionally underrepresented in science and engineering. This program enhances and emphasizes the importance the Foundation places on the development of full, balanced academic careers which include both research and education.