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(with Nicholas Ouellette)
Fluid flows have special topological features known as hyperbolic and elliptic points. In both cases, the fluid is instantaneously at rest locally; in the hyperbolic case fluid approaches along one line and departs along another, while near elliptic points, fluid circulates. We show how measurements of the time-dependent curvature of particle trajectories allow these special points to be detected and tracked over time. We show how the special points are created and annihilated in pairs, at a rate that depends on the Reynolds number. This approach leads to a novel method of characterizing spatiotemporally chaotic flow. Here, the flows have significant inertia, but the inertia of the tracers is relatively small. The current work focuses on two-dimensional flow, but the method could be extended to three dimensions in simulations. |
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