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New Evidence Of Discrete Scale Invariance In The Energy Dissipation Of Three-Dimensional Turbulence: Correlation Approach And Direct Spectral Detection

Author

Listed:
  • WEI-XING ZHOU

    (Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90095, USA)

  • DIDIER SORNETTE

    (Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90095, USA;
    Department of Earth and Space Sciences, University of California, Los Angeles, CA 90095, USA;
    Laboratoire de Physique de la Matière Condensée, CNRS UMR 6622 and Université de Nice-Sophia Antipolis, 06108 Nice Cedex 2, France)

  • VLADILEN PISARENKO

    (International Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Ac. Sci. Warshavskoye sh., 79, kor. 2, Moscow 113556, Russia)

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.

Suggested Citation

  • Wei-Xing Zhou & Didier Sornette & Vladilen Pisarenko, 2003. "New Evidence Of Discrete Scale Invariance In The Energy Dissipation Of Three-Dimensional Turbulence: Correlation Approach And Direct Spectral Detection," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 14(04), pages 459-470.
    • Handle: RePEc:wsi:ijmpcx:v:14:y:2003:i:04:n:s0129183103004632
    DOI: 10.1142/S0129183103004632
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    Citations

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    Cited by:

    1. Zhou, Wei-Xing & Sornette, Didier, 2003. "2000–2003 real estate bubble in the UK but not in the USA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 329(1), pages 249-263.
    2. Jiang, Zhi-Qiang & Ren, Fei & Gu, Gao-Feng & Tan, Qun-Zhao & Zhou, Wei-Xing, 2010. "Statistical properties of online avatar numbers in a massive multiplayer online role-playing game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(4), pages 807-814.
    3. Ji, Li-Jun & Zhou, Wei-Xing & Liu, Hai-Feng & Gong, Xin & Wang, Fu-Chen & Yu, Zun-Hong, 2009. "R/S method for unevenly sampled time series: Application to detecting long-term temporal dependence of droplets transiting through a fixed spatial point in gas–liquid two-phase turbulent jets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(17), pages 3345-3354.
    4. Vandermarliere, B. & Ryckebusch, J. & Schoors, K. & Cauwels, P. & Sornette, D., 2017. "Discrete hierarchy of sizes and performances in the exchange-traded fund universe," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 111-123.
    5. Sornette, Didier & Zhou, Wei-Xing, 2004. "Evidence of fueling of the 2000 new economy bubble by foreign capital inflow: implications for the future of the US economy and its stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 332(C), pages 412-440.
    6. Didier Sornette & Wei-Xing Zhou, 2003. "The US 2000-2002 market descent: clarification," Quantitative Finance, Taylor & Francis Journals, vol. 3(3), pages 39-41.
    7. Zhou, Wei-Xing & Sornette, Didier, 2009. "Numerical investigations of discrete scale invariance in fractals and multifractal measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(13), pages 2623-2639.

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