Fundamental Mathematical and Experimental Fluid Dynamics

本研究项目以数学流体力学理论与实验相结合的方式，探讨流体的基本现象。大部分理论和实验研究将在2007年6月开放的新北卡罗来纳大学跨学科流体实验室及其周围进行。该项目将涉及2名数学系教师、1名研究生和1名本科生进行实验和理论研究，旨在更好地理解分层和/或粘性系统的混合、夹带和流动特性。研究将包括通过密度分层评估Stokes流散度的正则化，具有刚性边界条件的有限时间增强扩散，时变剪切层存在下的球体流体动力学，以及奇异非自伴随微分特征值问题的分析。将探讨这些技术在自然科学中的应用。我们生活和呼吸的环境是一个复杂的耦合流体系统，其动力学具有在广泛的空间和时间尺度上发生的现象。从肺中最小的纤毛（为吸入污染物提供流体动力学防御机制）到大气、海洋和气候，我们直接与流体环境相互作用。该项目旨在为自然科学的本科生和研究生提供更好的科学理解，并在此过程中为研究和教育体验提供新的机会，并将通过参观和暑期研究实习向初中生和高中生伸出援助之手。该项目特别侧重于基础流体动力学的研究，重点是提高对不同环境（如大气、海洋和生物系统）中在分层流体中运动的浸入体之间相互作用的理解。这种行为的具体例子包括在海洋中沉淀的“海洋雪”，它负责从大气中隔离二氧化碳，以及形成水下被困的油羽，例如在墨西哥湾深水地平线石油泄漏事件中发生的那些。

This research project focuses on fundamental fluid phenomena explored through a combination of mathematical hydrodynamic theory and experiment. The majority of this theoretical and experimental research will take place in and around the new UNC Interdisciplinary fluids laboratory, which opened in June 2007. This project will involve 2 mathematics faculty, 1 graduate student, and 1 undergraduate student to perform experimental and theoretical research designed to better understand mixing, entrainment, and flow properties of stratified and/or viscous systems. Research will include assessing the regularization of Stokes flow divergences through density stratifications, finite time enhanced diffusion with rigid boundary conditions, the hydrodynamics of spheres in the presence of time varying shear layers, and the analysis of singular non-self adjoint differential eigenvalue problems. Applications of these techniques to the natural sciences will be explored. The environment in which we live and breathe is a complex coupled fluid system whose dynamics possess phenomena occurring on a vast range of space and time scales. From the smallest cilia in the lung which provide a hydrodynamic defense mechanism against inhaled contaminants to the atmosphere, oceans, and our climate, we interact directly with our fluid environment. The project seeks to provide both improved scientific understanding, and, along the way, new opportunities for research and educational experiences for undergraduate and graduate students of the natural sciences and will have an outreach to middle and high school students through tours and summer research internships. In particular, this project is focused upon research in fundamental fluid dynamics with emphasis on improved understanding of the interaction between immersed bodies moving in stratified fluids in different environments such as in atmospheres and oceans and in biological systems. Specific examples of such behavior include the settling of "marine snow" in the ocean which is responsible for sequestering carbon dioxide from the atmosphere, as well as the formation of underwater trapped oil plumes such as those occurring in the Deepwater Horizon Gulf of Mexico oil spill.