DynSyst_Special_Topics/Collaborative Research: A New Braid Theoretic Approach To Uncovering Transport Barriers In Complex Flows

DynSyst_Special_Topics/合作研究：一种揭示复杂流中传输障碍的新编织理论方法

• 批准号: 1233935
• 负责人: Jean-Luc Thiffeault
• 金额: $ 25.84万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-01 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1233935&HistoricalAwards=false
• 关键词: DynSyst_Special_Topics; Collaborative; Research; New; Braid

The research objective of this collaborative award is the advancement and application of a novel approach for identifying transport barriers in complex fluid flows based on the mathematical discipline of Braid Theory. This approach has the potential to enable a complex flow field to be decomposed into the key domains that organize material transport, using only sparse trajectory data. To investigate the utility and robustness of the approach, this collaborative research project will combine fundamental mathematical research with testing via laboratory experiments, numerical simulations, and field data sets. Deliverables include the development, validation and assessment of a new technique for identifying transport barriers in fluid flows, the creation of new fluid dynamics analysis tools, the training of a graduate student and a postdoc, research experience for undergraduate and high school students, and the organization of a major international workshop. Transport barriers organize material transport in the Earth's oceans, lakes and rivers. It is a longstanding challenge to identify these dynamical structures, however, since a principal source of data is the trajectories of Lagrangian drifters, which are inevitably sparsely distributed due to the large physical scales involved. The Braid Theory approach has the potential to extract valuable information on the shape and location of transport barriers from sparse drifter data sets. The resulting methodology also supports efficient, real-time implementation; a potentially transformative application is to improve time-sensitive decision-making strategies for man-made and naturally occurring environmental scenarios, including oil spills, radioactive leaks and algal blooms. The results will be disseminated to researchers in academia, government and industry, in particular via a week-long international workshop at the Banff Center, and the academic and personal careers of a high-school student, an undergraduate student, a graduate student and a postdoc will benefit from training in this field.

该协作奖项的研究目标是基于编织理论的数学学科识别复杂流体流中的运输障碍的新方法的进步和应用。这种方法有可能仅使用稀疏的轨迹数据将复杂的流场分解为组织材料传输的关键域。为了研究该方法的效用和鲁棒性，该协作研究项目将通过实验室实验，数值模拟和现场数据集将基本数学研究与测试相结合。可交付成果包括开发，验证和评估一种新技术，用于识别流体流中的运输障碍，新的流体动力学分析工具的创建，研究生的培训和博士后的培训，本科生和高中生的研究经验以及主要的国际研讨会的组织。运输障碍组织地球海洋，湖泊和河流中的材料运输。但是，确定这些动力学结构是一个长期的挑战，因为数据的主要来源是拉格朗日漂流者的轨迹，由于涉及大量的物理尺度，它们不可避免地分布得很少。辫子理论方法有可能从稀疏的漂流者数据集中提取有关传输壁垒的形状和位置的有价值的信息。最终的方法还支持有效的实时实施。一种潜在的变革应用是为了改善人造和自然发生的环境场景（包括漏油，放射性泄漏和藻类开花）的时间敏感决策策略。结果将被传播给学术界，政府和行业的研究人员，尤其是通过班夫中心为期一周的国际研讨会，以及一名高中生，一名本科生，研究生和博士学位的学术和个人职业将从该领域的培训中受益。