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Application of generalized thermostatistics to fully developed turbulence

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  • Beck, Christian

Abstract

We apply the formalism of non-extensive statistical mechanics to fully developed turbulent flows. We obtain analytical formulas for probability density functions of velocity differences depending on distance r/η and Reynolds number Rλ, which are in very good agreement with turbulence experiments. The skewness is taken into account by analysing universal contributions due to higher-order correlations of the chaotic dynamics. We also calculate the moment scaling exponents ζm, which also agree well with experimental data.

Suggested Citation

  • Beck, Christian, 2000. "Application of generalized thermostatistics to fully developed turbulence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 277(1), pages 115-123.
    • Handle: RePEc:eee:phsmap:v:277:y:2000:i:1:p:115-123
    DOI: 10.1016/S0378-4371(99)00508-7
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    Cited by:

    1. Quan, L. & Ferrero, E. & Hu, F., 2012. "Relating statistical moments and entropy in the stable boundary layer," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 231-247.
    2. Gravanis, E. & Akylas, E. & Michailides, C. & Livadiotis, G., 2021. "Superstatistics and isotropic turbulence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    3. Billio, Monica & Casarin, Roberto & Costola, Michele & Pasqualini, Andrea, 2016. "An entropy-based early warning indicator for systemic risk," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 45(C), pages 42-59.
    4. Asgarani, Somayeh, 2013. "A set of new three-parameter entropies in terms of a generalized incomplete Gamma function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(9), pages 1972-1976.

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