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

9701942麦克劳克林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。具体地说，这些研究工作概述了湍流传输和标量间歇的研究，预混燃烧中增强燃烧速度的数值计算，以及弱可压缩传输现象的理论和计算研究。这项工作的一个基本主题是隔离流体流动特性如何影响传输现象，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滞弹性热传输。这些研究涉及现代渐近、数值和概率技术的复杂整合。此外，该奖项还将支持继续开发本科生/研究生级别的高级数学流体力学课程。这门课程旨在向学生提供理解流体力学所需的基本数学工具，并迅速装备学生解决应用数学研究问题的基本技能。此外，还将开发一个小型流体演示实验室，以提供许多流体现象的可视化。该学院早期职业发展奖将为首席研究员提供机会，在开发新的教育课程的同时，继续他在理解许多流体传输现象方面的研究努力。发展合理的流体传输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，量化流体流动特性如何影响此类染料的混合是至关重要的。此外，声音传输理论的发展自然会产生对各种混合应用的洞察，例如跟踪大气污染物。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信息，在这些模型中，一个常见的困难是如何处理无法解析的长度和时间尺度。计算流体力学中公认的事实是，存在着重要的、不可忽视的、复杂的流体现象，即使是最大的超级计算机也无法解决这些现象。这些子网格效果在许多流体应用中扮演着重要的角色，例如天气预报。它们不能被忽视，一个标准的方法是用更简单的东西来取代它们--一个有效的混合系数。在许多应用中，这里开发的输运理论为这些系数提供了合理的理由和量化，并可能对现有的计算模型提供改进。最后，课程工作将涉及开发一个小型流体实验室，其中包括一个示范水洞。通过这个实验，学习流体理论的学生将发现与实际流体现象的令人兴奋的视觉接触，这种视觉接触在数学课程中通常是不存在的，这种可视化将导致对数学理论在理解可观察现象中的有用性的更大的兴奋和欣赏。国家科学基金会强烈鼓励学术人员的早期发展，既是教育工作者，也是研究者。学院早期职业发展(Career)计划是一个基础范围的计划，为初级教师在其整体职业发展的背景下提供支持。它在一个单一的计划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。这一计划加强并强调了基金会对充分、平衡的学术事业发展的重视，包括研究和教育。

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.