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New Evidence of Discrete Scale Invariance in the Energy Dissipation of Three-Dimensional Turbulence: Correlation Approach and Direct Spectral Detection | | W.-X. Zhou
; D. Sornette
; V. Pisarenko
; | | Date: |
18 Aug 2002 | | Journal: | Int. J. Modern Phys. C 14 (4), 459-470 (2003) | | Subject: | Statistical Mechanics | cond-mat.stat-mech | | 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 $gamma = 2.008 pm 0.006$. | | Source: | arXiv, cond-mat/0208347 | | Services: | Forum | Review | PDF | Favorites | |
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