Complex Networks Unveiling Spatial Patterns in Turbulence

TL;DR

This paper introduces a complex network-based method to analyze turbulence data, revealing spatial patterns and regions in turbulent flows, which enhances understanding of large-scale turbulent structures.

Contribution

It applies complex network theory to turbulence analysis, introducing a new parameter for pattern size, and systematically identifies spatial regions in turbulent flows.

Findings

Degree centrality highlights spatial patterns moving with similar vorticity.

Pattern size varies from small to intermediate scales.

Network analysis provides new insights into turbulent flow structures.

Abstract

Numerical and experimental turbulence simulations are nowadays reaching the size of the so-called big data, thus requiring refined investigative tools for appropriate statistical analyses and data mining. We present a new approach based on the complex network theory, offering a powerful framework to explore complex systems with a huge number of interacting elements. Although interest on complex networks has been increasing in the last years, few recent studies have been applied to turbulence. We propose an investigation starting from a two-point correlation for the kinetic energy of a forced isotropic field numerically solved. Among all the metrics analyzed, the degree centrality is the most significant, suggesting the formation of spatial patterns which coherently move with similar vorticity over the large eddy turnover time scale. Pattern size can be quantified through a newly-introduced parameter (i.e., average physical distance) and varies from small to intermediate scales. The network analysis allows a systematic identification of different spatial regions, providing new insights into the spatial characterization of turbulent flows. Based on present findings, the application to highly inhomogeneous flows seems promising and deserves additional future investigation.