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

这项工作得到了国家科学基金会教师早期职业发展奖的支持。研究部分将侧重于对流体现象的理论理解。具体来说，这些研究工作概述了湍流输运和标量间歇的研究，预混燃烧中增强燃烧速度的数值计算，以及弱可压缩输运现象的理论和计算研究。这项工作的一个基本主题是分离流体流动特性如何影响输运现象，这可能包括增强的混合速率、增强的罕见事件概率、增强的燃烧速度和增强的非弹性热输运。这些研究涉及现代渐近、数值和概率技术的复杂集成。此外，该奖项将支持高级本科/研究生水平的数学流体动力学课程的持续课程开发。这样的课程旨在为学生提供必要的数学工具，以理解流体力学，并迅速装备学生的基本技术，以解决应用数学研究问题。此外，一个小的演示流体实验室将开发提供可视化的许多流体现象。这个学院早期职业发展奖将为首席研究员提供机会，在了解许多流体输送现象的同时，继续他的研究工作，同时开发新的教育课程。发展流体输运的合理理论在许多方面都是基本的。对流体湍流的实验理解通常涉及对被动染料的跟踪，因此，对流体流动特性如何影响这种染料的混合进行量化是至关重要的。此外，声输运理论的发展自然会产生对各种混合应用的见解，例如大气污染物的跟踪。也许最重要的是，这些理论可能为大规模计算流体、燃烧和气候模型提供潜在的信息，在这些模型中，一个共同的困难是如何处理不可解决的长度和时间尺度。在计算流体动力学中，存在一些重要的、不可忽略的、复杂的流体现象，这些现象即使在最大的超级计算机上也无法解决，这是一个公认的事实。这些子网格效应在许多流体应用中发挥着重要作用，例如天气预报。它们不能被忽略，标准的方法是用更简单的东西来代替它们——有效的混合系数。在许多应用中，这里发展的输运理论为这些系数提供了合理的理由和量化，并可能为现有的计算模型提供改进。最后，课程的努力将涉及一个小型流体实验室的发展，包括一个示范水洞。通过这个实验，学习流体理论的学生将发现与数学课程中通常无法获得的真实流体现象的令人兴奋的视觉接触，这种可视化将导致更大的兴奋和欣赏数学理论在理解可观察现象中的有用性。美国国家科学基金会强烈鼓励教师作为教育工作者和研究人员的早期发展。教师早期职业发展（Career）计划是一个基金会范围内的计划，为初级教师的整体职业发展提供支持。它在一个项目中结合了对最广泛意义上的高质量研究和教育的支持，以及那些传统上在科学和工程领域代表性不足的人的充分参与。该计划加强并强调了基金会对包括研究和教育在内的全面，平衡的学术生涯发展的重要性。

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.