Flow networks: A characterization of geophysical fluid transport

Ser-Giacomi, Enrico; Rossi, Vincent; Lopez, Cristobal; Hernandez-Garcia, Emilio
Chaos 25, 036404 (1-18) (2015)

We represent transport between different regions of a fluid
domain by flow networks, constructed from the discrete
representation of the Perron-Frobenius or transfer operator
associated to the fluid advection dynamics. The procedure is
useful to analyze fluid dynamics in geophysical contexts, as
illustrated by the construction of a flow network associated to
the surface circulation in the Mediterranean sea. We use
network-theory tools to analyze the flow network and gain
insights into transport processes. In particular we
quantitatively relate dispersion and mixing characteristics,
classically quantified by Lyapunov exponents, to the degree of
the network nodes. A family of network entropies is
defined from the network adjacency matrix, and related to the
statistics of stretching in the fluid, in particular to the
Lyapunov exponent field. Finally we use a network community
detection algorithm, Infomap, to partition the
Mediterranean network into coherent regions, i.e. areas
internally well mixed, but with little fluid interchange
between them.

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