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| Most geometric and operator methods for analysis of flows depend on ability to evaluate the flow on a fairly dense set of points. When information about the flow is very sparsely sampled, e.g., oceanographic data coming from profiling floats, alternative methods are needed. The braid dynamics approach takes a sparse set of Lagrangian trajectories and represents it by an algebraic braid, a "data structure" that keeps track of a relative ordering of Lagrangian particles and the sequence of their interchanges over time. From previous work on stirring problems, it is known that this approach successfully estimates the amount of mixing in a flow when a particular set of periodic Lagrangian trajectories is used, e.g., trajectories of rods used to stir the flow. In this presentation, we discuss the efforts to extend the understanding of braid dynamics for problems in which a distinguished periodic trajectory set does not exist, or when it is not known a priori. Our intended application problems are oceanic flows, where trajectory data is often of finite length, sparse, non-periodic, and no distinguished trajectories are known. |
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