Network-based measure of the finite size Lyapunov exponent

Antich Navarro, Joan (supervisors Enrico Ser-Giacomi and Cristobal Lopez))
Master Thesis (2022)

Fluid dynamics is concerned with the analysis of fluid flows and the characterization of its properties. Although classical approaches have used the methodology of Dynamical Systems' theory (DS) to characterize Lagrangian transport, a new Complex Network (CN) based approach is starting to gain relevance, specifically for spatially distributed flows. The fact that both approaches are able to characterize the same system allows us to think that their measures and concepts may be transferable from one to the other. Indeed, a dictionary relating measures performed from each framework is in construction. So far only for the Finite Time Lyapunov Exponent(FTLE), a measure from the framework of DS, relations to CN-based measures such as the degree and betweenness centrality have been established. In this work, we want to contribute further expanding the list of relations between both worlds, showing that a relation between a network-based measure and the Finite Size Lyapunov Exponent (FSLE) is very plausible to be established.

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