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Proof of Hopf’s Conjecture on the Structure of Turbulence (in Memory of Tatarsky)

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Abstract

The paper is dedicated to the memory of V.I. Tatarsky (1929–2020); however, it is not a personalia. We present, as a brief review of our scientific works, the experimental and theoretical proofs of E. Hopf’s conjecture (1948) about the structure of turbulence as a space-time chaos of a finite number of interacting coherent structures. This review is the result of our many years research in the theory of turbulence. It is the theory of turbulence that the authors have chosen as a scientific direction under the scientific influence of V.I. Tatarsky.

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Funding

The work was carried out within the scientific program of the National Center for Physics and Mathematics (project “Physics of high energy densities. Stage 2023–2025”) in regards to the computational-theoretical analysis of coherent components of turbulence spectra and effects of intermittency of turbulence and attenuation of light fluctuations. The development of the technique of measurements, analysis, and calculations was supported by the Ministry of Science and Higher Education of the Russian Federation (V.E. Zuev Institute of Atmospheric Optics, Siberian Branch, Russian Academy of Sciences).

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Authors and Affiliations

  1. V.E. Zuev Institute of Atmospheric Optics, Siberian Branch, Russian Academy of Sciences, 634055, Tomsk, Russia

    V. V. Nosov, V. P. Lukin, E. V. Nosov & A. V. Torgaev

  2. Institute of Solar-Terrestrial Physics, Siberian Branch, Russian Academy of Sciences, 664033, Irkutsk, Russia

    P. G. Kovadlo

Authors
  1. V. V. Nosov
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  2. V. P. Lukin
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  3. P. G. Kovadlo
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  4. E. V. Nosov
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  5. A. V. Torgaev
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Corresponding authors

Correspondence to V. V. Nosov, V. P. Lukin, P. G. Kovadlo, E. V. Nosov or A. V. Torgaev.

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The authors declare that they have no conflicts of interest.

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Translated by A. Nikol’skii

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Nosov, V.V., Lukin, V.P., Kovadlo, P.G. et al. Proof of Hopf’s Conjecture on the Structure of Turbulence (in Memory of Tatarsky). Atmos Ocean Opt 36, 300–305 (2023). https://doi.org/10.1134/S1024856023040139

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  • DOI: https://doi.org/10.1134/S1024856023040139

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