Discussion and Visualization of Distinguished Hyperbolic Trajectories as a Generalization of Critical Points to 2D Time-dependent Flow

Roxana Bujack

View presentation:2022-10-17T21:13:00ZGMT-0600Change your timezone on the schedule page
2022-10-17T21:13:00Z
Exemplar figure, described by caption below
Top row: different time steps of a saddle under accelerated rotation visualized using LIC. Middle row: the trajectory of the approximate DHT computed with the algorithm by Ju et al. on top of the instantaneous velocity of the field from its perspective computed with our algorithm. Bottom row: the trajectory of the true DHT on top of the instantaneous velocity of the field from the DHT’s perspective computed with our algorithm.

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Keywords

visualization, vector field, flow, topology, Lagrangian, objective, time-dependent, distinguished hyperbolic trajectory

Abstract

Classical vector field topology has proven to be a useful visualization technique for steady flow, but its straightforward application to time-dependent flows lacks physical meaning. Necessary requirements for physical meaningfulness include the results to be objective, i.e., independent of the frame of reference of the observer, and Lagrangian, i.e., that the generalized critical points are trajectories. We analyze whether the theoretical concept of distinguished hyperbolic trajectories provides a physically meaningful generalization to classical critical points and if the existing extraction algorithms correctly compute what has been defined mathematically. We show that both theory and algorithms constitute a significant improvement over previous methods. We further present a method to visualize a time-dependent flow field in the reference frames of distinguished trajectories. The result is easy to interpret because it makes these trajectories look like classical critical points for each instance in time, but it is meaningful because it is Lagrangian and objective.