From network theory to dynamical systems and back: Lagrangian Betweenness reveals bottlenecks in geophysical flows

Abstract

Transport phenomena, including diffusion, mixing, spreading, and mobility, are crucial to understand and model dynamical features of complex systems. In particular, the study of geophysical flows attracted a lot of interest in the last decades as fluid transport has proven to play a fundamental role in climatic and environmental research across a wide range of scales. Two theoretical frameworks have been effectively used to investigate transport phenomena in complex systems: Dynamical Systems Theory (DST) and Network Theory (NT). However, few explicit connections between these two different views have been established. Here, we focus on the betweenness centrality, a widely used local measure which characterizes transport and connectivity in NT. By linking analytically DST and NT we provide a novel, continuous-in-time formulation of betweenness, called Lagrangian Betweenness, as a function of Lyapunov exponents. This permits to quantitatively relate hyperbolic points and heteroclinic connections in a given dynamical system to the main transport bottlenecks of its associated network. Moreover, using modeled and observational velocity fields, we show that such bottlenecks are present and surprisingly persistent in the oceanic circulation illustrating their importance in organizing fluid motion. The link between DST and NT rooted in the definition of the Lagrangian Betweenness has the potential to promote further theoretical developments and applications at the interface between these two fields. Finally, the identification of such circulation hotspots provides new crucial information about transport processes in geophysical flows and how they control the redistribution of various tracers of climatic (e.g. heat, carbon, moisture), biological (e.g. larvae, pathogens) and human (e.g. pollutants, plastics) interests.N