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Third International Workshop

NONLINEAR PROCESSES IN OCEANIC AND ATMOSPHERIC FLOWS


6-8 July 2016 | ICMAT, Campus Cantoblanco UAM, Madrid, Spain



Lagrangian Flow Network: theory and applications



Author

Vincent Rossi (IFISC (CSIC-UIB)). Enrico Ser-Giacomi, Pedro Monroy, Mélodie Dubois, Emilio Hernandez-García, Cristóbal López


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Abstract


The last two decades have seen important advances in the Lagrangian description of transport and mixing in fluid flows driven by concepts from dynamical systems theory. In the meantime, Network Theory approaches continue arousing scientific interests and have been successfully used, among other, for geophysical systems with climate networks. Linking the network formalism with transport and mixing phenomena in geophysical flows, we develop a new paradigm which we call Lagrangian Flow Network. It consists in analyzing a directed, weighted, spatially embedded and time-dependent network which describes the material fluid flow among different locations. We relate theoretically dispersion and mixing characteristics, classically quantified by Lyapunov exponents, to the degree of the network nodes and then to a family of network entropies defined from the network adjacency matrix. Among possible applications, this new framework allows studying the connectivity and structural complexity of marine populations by providing a systematic characterization of larval transport and dispersal. The simulated networks are composed of an ensemble of oceanic sub-regions which are interconnected through the transport of larvae by ocean currents. The analysis of such networks allows the identification of hydrodynamical provinces (coherent oceanic regions, i.e. areas internally well mixed, but with little fluid or larvae interchange between them) and the computation of connectivity proxies measuring retention and exchange of larvae at multiple scales. These diagnostics, whose sensitivity and robustness have been tested, provide useful information to design management and protection plans for marine ecosystems.

The last two decades have seen important advances in the Lagrangian description of transport and mixing in fluid flows driven by concepts from dynamical systems theory. In the meantime, Network Theory approaches continue arousing scientific interests and have been successfully used, among other, for geophysical systems with climate networks. Linking the network formalism with transport and mixing phenomena in geophysical flows, we develop a new paradigm which we call Lagrangian Flow Network. It consists in analyzing a directed, weighted, spatially embedded and time-dependent network which describes the material fluid flow among different locations. We relate theoretically dispersion and mixing characteristics, classically quantified by Lyapunov exponents, to the degree of the network nodes and then to a family of network entropies defined from the network adjacency matrix. Among possible applications, this new framework allows studying the connectivity and structural complexity of marine populations by providing a systematic characterization of larval transport and dispersal. The simulated networks are composed of an ensemble of oceanic sub-regions which are interconnected through the transport of larvae by ocean currents. The analysis of such networks allows the identification of hydrodynamical provinces (coherent oceanic regions, i.e. areas internally well mixed, but with little fluid or larvae interchange between them) and the computation of connectivity proxies measuring retention and exchange of larvae at multiple scales. These diagnostics, whose sensitivity and robustness have been tested, provide useful information to design management and protection plans for marine ecosystems.


Presentation PDF