New Evidence of Discrete Scale Invariance in the Energy Dissipation of Three-Dimensional Turbulence: Correlation Approach and Direct Spectral Detection

TL;DR

This paper provides new evidence of discrete scale invariance in the energy dissipation of 3D turbulence, using correlation-based and spectral methods to detect log-periodic corrections and harmonics in experimental data.

Contribution

It introduces a simplified averaging and spectral analysis approach that strengthens the detection of log-periodic oscillations in turbulence energy dissipation.

Findings

Significant log-periodic corrections to scaling are confirmed.

More than 20 harmonics of a fundamental frequency are detected.

The fundamental logarithmic frequency corresponds to a scaling ratio of approximately 2.

Abstract

We extend the analysis of [Zhou and Sornette, Physica D 165, 94-125, 2002] showing statistically significant log-periodic corrections to scaling in the moments of the energy dissipation rate in experiments at high Reynolds number ($\approx 2500$) of three-dimensional fully developed turbulence. First, we develop a simple variant of the canonical averaging method using a rephasing scheme between different samples based on pairwise correlations that confirms Zhou and Sornette's previous results. The second analysis uses a simpler local spectral approach and then performs averages over many local spectra. This yields stronger evidence of the existence of underlying log-periodic undulations, with the detection of more than 20 harmonics of a fundamental logarithmic frequency $f = 1.434 \pm 0.007$ corresponding to the preferred scaling ratio $\gamma = 2.008 \pm 0.006$.