Flow networks: A characterization of geophysical fluid transport

TL;DR

This paper introduces a novel approach using flow networks derived from transfer operators to analyze geophysical fluid transport, providing insights into mixing, dispersion, and coherent region detection in oceanic flows.

Contribution

It presents a new method to characterize fluid transport by constructing flow networks from transfer operators, linking network properties to fluid stretching and mixing.

Findings

Flow networks effectively represent geophysical fluid transport.

Network entropies relate to fluid stretching and Lyapunov exponents.

Community detection identifies coherent regions in the Mediterranean Sea.

Abstract

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.