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

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 $\gamma =2.008\pm 0.006$.

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References in corpus (3)

• The multifractal nature of turbulent energy dissipation
• Statistical Significance of Periodicity and Log-Periodicity with Heavy-Tailed Correlated Noise
• Evidence of Intermittent Cascades from Discrete Hierarchical Dissipation in Turbulence

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