Visibility graph analysis of wall turbulence time-series

TL;DR

This paper applies the natural visibility graph method to analyze wall turbulence time-series, revealing key temporal features and their variation across the flow's wall-normal direction, offering a new tool for turbulence analysis.

Contribution

It introduces the use of visibility graph metrics to characterize turbulence time-series and demonstrates their effectiveness in capturing flow features across the wall-normal coordinate.

Findings

Visibility metrics vary with wall-normal position, revealing flow structure.

The method uncovers temporal properties linked to turbulence features.

Visibility graphs provide a promising tool for turbulence time-series analysis.

Abstract

The spatio-temporal features of the velocity field of a fully-developed turbulent channel flow are investigated through the natural visibility graph (NVG) method, which is able to fully map the intrinsic structure of the time-series into complex networks. Time-series of the three velocity components, (u,v,w), are analyzed at fixed grid-points of the whole three-dimensional domain. Each time-series was mapped into a network by means of the NVG algorithm, so that each network corresponds to a grid-point of the simulation. The degree centrality, the transitivity and the here proposed mean link-length were evaluated as indicators of the global visibility, inter-visibility, and mean temporal distance among nodes, respectively. The metrics were averaged along the directions of homogeneity (x, z) of the flow, so they only depend on the wall-normal coordinate, y^+. The visibility-based networks, inheriting the flow field features, unveil key temporal properties of the turbulent time-series and their changes moving along y^+. Although intrinsically simple to be implemented, the visibility graph-based approach offers a promising and effective support to the classical methods for accurate time-series analyses of inhomogeneous turbulent flows.