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Analysis of turbulence by statistics based on generalized entropies

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  • Arimitsu, Toshihico
  • Arimitsu, Naoko

Abstract

An analytical formula of the scaling exponents of velocity structure function for fully developed turbulence is derived, non-perturbatively, by assuming that its underlying statistics is the one based on the generalized measures of entropy, the Renyi entropy or the Havrda–Charvat–Tsallis (HCT) entropy. It is revealed by a self-consistent analysis for the observed value μ=0.220(±1%) that the formula explains experimental data very well with single value, q=0.343, of the index which appears in the measures of the Renyi entropy or of the HCT entropy. The probability density functions of the velocity fluctuation and of the velocity gradient are also presented.

Suggested Citation

  • Arimitsu, Toshihico & Arimitsu, Naoko, 2001. "Analysis of turbulence by statistics based on generalized entropies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(1), pages 177-194.
    • Handle: RePEc:eee:phsmap:v:295:y:2001:i:1:p:177-194
    DOI: 10.1016/S0378-4371(01)00072-3
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    Cited by:

    1. Pavlos, G.P. & Iliopoulos, A.C. & Zastenker, G.N. & Zelenyi, L.M. & Karakatsanis, L.P. & Riazantseva, M.O. & Xenakis, M.N. & Pavlos, E.G., 2015. "Tsallis non-extensive statistics and solar wind plasma complexity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 422(C), pages 113-135.
    2. Iliopoulos, A.C. & Aifantis, E.C., 2018. "Tsallis q-triplet, intermittent turbulence and Portevin–Le Chatelier effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 498(C), pages 17-32.
    3. Hoyos, Isabel & Rodríguez, Boris Anghelo, 2020. "Drawing the complexity of Colombian climate from non-extensive extreme behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 548(C).
    4. Pavlos, G.P. & Karakatsanis, L.P. & Xenakis, M.N., 2012. "Tsallis non-extensive statistics, intermittent turbulence, SOC and chaos in the solar plasma, Part one: Sunspot dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6287-6319.
    5. A. Hoseinzadeh & G. Mohtashami Borzadaran & G. Yari, 2012. "Aspects concerning entropy and utility," Theory and Decision, Springer, vol. 72(2), pages 273-285, February.
    6. Karakatsanis, L.P. & Pavlos, G.P. & Xenakis, M.N., 2013. "Tsallis non-extensive statistics, intermittent turbulence, SOC and chaos in the solar plasma. Part two: Solar flares dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(18), pages 3920-3944.
    7. Ausloos, M., 2012. "Measuring complexity with multifractals in texts. Translation effects," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1349-1357.

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