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Abstract

The detection of Lagrangian Coherent Structure (LCS) is an important challenge in fluid dynamics, particularly in oceanography applications. For instance, knowledge of how regions of fluid are isolated from each other allows predictions of where damaging contaminants in the ocean or atmosphere will end up. Traditional trajectory analysis focuses on full trajectory histories that yield convoluted ?spaghetti plots?, that are hard to interpret. Fluid dynamics has given rise to the concept of LCS, which provides a new way of understanding transport in complex fluid flow. Existing method detect LCS, by examining the stretching field as given by finite-time Lyaponov exponents. These methods are very effective under the action of the velocity field, but many applications have a small number of particles of flow trajectories are known, for example when dealing with oceanic float data. We present a topological method for detecting invariant regions based on a small set of trajectories. In the method we regard the two-dimensional trajectory data as a braid in three dimensions, with time being the third coordinate. Invariant regions then correspond to trajectories that travel together and do not entangle other trajectories. We detect these regions by examining the growth of hypothetical loops surrounding sets of trajectories, and searching for loops that show negligible growth.

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