Topology of dynamical reconstructions from Lagrangian data

Abstract

Branched Manifold Analysis through Homologies (BraMAH) is a technique that computes the state-space topology of a dynamical reconstruction from scalar data. This work introduces the application of this technique to Lagrangian time series. The approach unveils the topological structure underlying the behavior of a fluid particle. When applied to a set of sparse particles, the results of the analysis can be used to classify them according to the dynamics they deploy during a given time window. Topological grids can be constructed to portray the spatial organization of the topological classes. The connection between the topological grids and the transport properties of the flow is examined using streaklines. Even if demonstrated here in the context of kinematic flow models, the generality of the method allows for its potential application to experimental or observational Lagrangian data satisfying the technical requirements for the analysis.