TY - JOUR T1 - Local Trajectory Variation Exponent (LTVE) for Visualizing Dynamical Systems AU - Tsai , Yun Chen AU - Leung , Shingyu JO - Communications in Computational Physics VL - 5 SP - 1411 EP - 1439 PY - 2024 DA - 2024/12 SN - 36 DO - http://doi.org/10.4208/cicp.OA-2023-0221 UR - https://global-sci.org/intro/article_detail/cicp/23613.html KW - Lagrangian coherent structure, trajectory metric, trajectory analysis, finite time Lyapunov exponent. AB -

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.