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Local Trajectory Variation Exponent (LTVE) for Visualizing Dynamical Systems

Local Trajectory Variation Exponent (LTVE) for Visualizing Dynamical Systems

Year:    2024

Author:    Yun Chen Tsai, Shingyu Leung

Communications in Computational Physics, Vol. 36 (2024), Iss. 5 : pp. 1411–1439

Abstract

The identification and visualization of Lagrangian structures in flows plays a crucial role in the study of dynamic systems and fluid dynamics. The Finite Time Lyapunov Exponent (FTLE) has been widely used for this purpose; however, it only approximates the flow by considering the positions of particles at the initial and final times, ignoring the actual trajectory of the particle. To overcome this limitation, we propose a novel quantity that extends and generalizes the FTLE by incorporating trajectory metrics as a measure of similarity between trajectories. Our proposed method utilizes trajectory metrics to quantify the distance between trajectories, providing a more robust and accurate measure of the LCS. By incorporating trajectory metrics, we can capture the actual path of the particle and account for its behavior over time, resulting in a more comprehensive analysis of the flow. Our approach extends the traditional FTLE approach to include trajectory metrics as a means of capturing the complexity of the flow.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2023-0221

Communications in Computational Physics, Vol. 36 (2024), Iss. 5 : pp. 1411–1439

Published online:    2024-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    29

Keywords:    Lagrangian coherent structure trajectory metric trajectory analysis finite time Lyapunov exponent.

Author Details

Yun Chen Tsai

Shingyu Leung