Fully Developed Turbulence in the view of Horizontal Visibility Graphs

TL;DR

This paper uses horizontal visibility graphs to analyze turbulent flow data, revealing universal network features in velocity fluctuations and Reynolds number-dependent properties in acceleration series, highlighting transitional behaviors.

Contribution

It introduces a novel approach of mapping turbulence time series onto complex networks, uncovering universal and transitional features related to Reynolds number.

Findings

Velocity fluctuations exhibit universal network topology.

Acceleration series show Reynolds number-dependent stretched exponential degree distributions.

Network features indicate a transitional behavior with changing Reynolds number.

Abstract

We employ the horizontal visibility algorithm to map the velocity and acceleration time series in turbulent flows with different Reynolds numbers, onto complex networks. The universal nature of velocity fluctuations in high Reynolds turbulent Helium flow is found to be inherited in the corresponding network topology. The degree distributions of the acceleration series are shown to have stretched exponential forms with the Reynolds number dependent fitting parameter. Furthermore, for acceleration time series, we find a transitional behavior in terms of the Reynolds number in all network features which is in agreement with recent empirical studies.