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

该合作奖的研究目标是基于编织理论的数学学科，提出并应用一种新的方法来识别复杂流体流动中的传输障碍。这种方法有可能只使用稀疏的轨迹数据，将复杂的流场分解成组织材料运输的关键区域。为了研究这种方法的实用性和稳健性，这个合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础数学研究与测试相结合。交付成果包括开发、验证和评估确定流体流动中传输障碍的新技术，创建新的流体动力学分析工具，培训研究生和博士后，为本科生和高中生提供研究经验，以及组织一次重要的国际研讨会。运输障碍组织了地球上海洋、湖泊和河流中的物质运输。然而，确定这些动力学结构是一个长期的挑战，因为一个主要的数据来源是拉格朗日漂移者的轨迹，由于涉及的物理尺度很大，这些轨迹不可避免地是稀疏分布的。辫子理论方法有可能从稀疏的漂移数据集中提取关于运输障碍的形状和位置的有价值的信息。由此产生的方法还支持高效、实时的实施；一个潜在的变革性应用是改进对时间敏感的决策战略，以应对包括漏油、放射性泄漏和藻类水华在内的人为和自然发生的环境情景。研究结果将传播给学术界、政府和工业界的研究人员，特别是通过在班夫中心举行的为期一周的国际研讨会，高中生、本科生、研究生和博士后的学术和个人职业生涯将从这一领域的培训中受益。

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.