NEW EVIDENCE OF DISCRETE SCALE INVARIANCE IN THE ENERGY DISSIPATION OF THREE-DIMENSIONAL TURBULENCE: CORRELATION APPROACH AND DIRECT SPECTRAL DETECTION

Wei-Xing Zhou, Didier Sornette () and Vladilen Pisarenko
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Didier Sornette: Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90095, USA;
Vladilen Pisarenko: International Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Ac. Sci. Warshavskoye sh., 79, kor. 2, Moscow 113556, Russia

International Journal of Modern Physics C (IJMPC), 2003, vol. 14, issue 04, 459-470

Abstract: 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(≈ 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 frequencyf = 1.434 ± 0.007corresponding to the preferred scaling ratioγ = 2.008 ± 0.006.

Keywords: Discrete scale invariance; log-periodicity; turbulence; energy dissipation; canonical averaging; Richardson–Kolmogorov cascade; 47.27.-i; 05.45.Df (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (7)

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DOI: 10.1142/S0129183103004632

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