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

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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.