Templex for Lagrangian dynamics in the Southwestern Atlantic

This work presents the first application of the templex approach to observational datasets, using Lagrangian trajectories obtained from satellite altimetry in the ocean. The templex is a recent topological construct that extends classical ideas from template theory to higher-dimensional systems. Unlike other methods in topological data analysis, which lack flow information, a templex encodes both the structure of phase space through a branched manifold analysis through homologies cell complex and the organization of flow cycles upon it through a directed graph defined on its highest-dimensional cells. As shown in earlier works, the description of flows in phase space indirectly enables a description of fluid flows in physical space, since particles sharing the same dynamics are known to move coherently. Particle sets in the Southwestern Atlantic Ocean are analyzed, revealing that the Lagrangian finite-time dynamics in this region can be related to those produced by a nonautonomous meandering jet model. We distinguished non-mixing (regular) islands from the chaotic sea. The results are also compared to those obtained from metric methods describing material transport in fluid flows and to the spatial organization of chlorophyll-a concentration. The seasonal variability of chaotic dynamics is also discussed.