New evidence of discrete scale invariance in the energy dissipation of three-dimensional turbulence: Correlation approach and direct spectral detection
We extend the analysis of Ref. 16 showing statistically significant log-periodic corrections to scaling in the moments of the energy dissipation rate in experiments at high Reynolds number (approximate to 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 +/- 0.007 corresponding to the preferred scaling ratio gamma = 2.008 +/- 0.006.
discrete scale invariance energy dissipation turbulence log-periodicity canonical averaging richardson-kolmogorov cascade