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PDF of velocity fluctuation in turbulence by a statistics based on generalized entropy

Author

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  • Arimitsu, Toshihico
  • Arimitsu, Naoko

Abstract

An analytical formula for the probability density function (PDF) of the velocity fluctuation in fully-developed turbulence is derived, non-perturbatively, by assuming that its underlying statistics is the one based on the generalized measures of entropy, the Rényi entropy or the Tsallis entropy. The parameters appearing in the PDF, including the index q in the generalized measures, are determined self-consistently with the help of the observed value μ of the intermittency exponent. The derived PDF explains quite well the experimentally observed density functions.

Suggested Citation

  • Arimitsu, Toshihico & Arimitsu, Naoko, 2002. "PDF of velocity fluctuation in turbulence by a statistics based on generalized entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 305(1), pages 218-226.
    • Handle: RePEc:eee:phsmap:v:305:y:2002:i:1:p:218-226
    DOI: 10.1016/S0378-4371(01)00665-3
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    Cited by:

    1. Sunoj, S.M. & Krishnan, Aswathy S. & Sankaran, P.G., 2018. "A quantile-based study of cumulative residual Tsallis entropy measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 410-421.
    2. Kozaki, M. & Sato, A.-H., 2008. "Application of the Beck model to stock markets: Value-at-Risk and portfolio risk assessment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1225-1246.
    3. Gravanis, E. & Akylas, E. & Michailides, C. & Livadiotis, G., 2021. "Superstatistics and isotropic turbulence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).

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