Statistical properties of visibility graph of energy dissipation rates in three-dimensional fully developed turbulence

TL;DR

This paper analyzes the statistical properties of visibility graphs constructed from energy dissipation rates in 3D turbulence, revealing power-law degree distribution, non-self-similarity, and allometric scaling.

Contribution

It introduces a novel analysis of turbulence data using visibility graphs, uncovering their degree distribution, self-similarity properties, and scaling behavior.

Findings

Degree distribution follows a power-law with exponent 3.0.

Network is not self-similar, shown by box-counting analysis.

Skeleton exhibits allometric scaling with exponent approximately 1.163.

Abstract

We study the statistical properties of the network constructed from the energy dissipation rate time series in the three dimensional developed turbulence using the visibility algorithm. The degree distribution is found to have a power-law tail with the tail exponent $\alpha=3.0$. The exponential relationship between the number of the boxes $N_B$ and the box size $l_B$ in the edge-covering box-counting method illustrates that the network is not self-similar, which is also confirmed by the hub-hub attraction according to the visibility algorithm. In addition, it is found that the skeleton of the visibility network exhibits excellent allometric scaling with the scaling exponent $\eta=1.163\pm0.005$.