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The uncertainty relation in the turbulent continuous medium

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Abstract

One of the key problems of continuum physics is the problem of determining the characteristics of disturbances, leading to chaos (turbulence) in the medium. Until now, the existing theories have not yielded results. In this paper, the uncertainty relation in the process of turbulence of a continuum medium is determined on the basis of stochastic equations and equivalence of measures. The uncertainty relation expresses the fact that there is not one vortex, but a family of vortices that have a single dependence of the space–energy similarity \(({E}\cdot {L}^{-{{a}}})\) = constant which are able to generate turbulence during the interaction with the main motion. The validity of the obtained uncertainty relation is confirmed by the satisfactory agreement of the obtained stochastic spectrum formulas with the experimental spectrum for turbulent flows in the pipe and on the flat plate. This family of vortexes has a formula of spectrum E(k) depending on wave numbers k in form \(E(k) \sim k^ n\). For the flow in the boundary layer on the flat plate \(n = -1.5\) and for the flow in the round tube \(n = -1.29 \div -1.4\).

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Acknowledgements

This work was supported by the program of increasing the competitive ability of National Research Nuclear University MEPhI (agreement with the Ministry of Education and Science of the Russian Federation of August 27, 2013, Project No. 02.a03.21.0005).

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Authors and Affiliations

  1. Department of Thermal Physics, National Research Nuclear University (MEPhI), Kashirskoye Shosse 31, Moscow, Russian Federation, 115409

    Artur V. Dmitrenko

  2. Department of Power Engineering, Russian University of Transport (MIIT), Obraztsova Street 9, Moscow, Russian Federation, 127994

    Artur V. Dmitrenko

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Correspondence to Artur V. Dmitrenko.

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Communicated by Andreas Öchsner.

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Dmitrenko, A.V. The uncertainty relation in the turbulent continuous medium. Continuum Mech. Thermodyn. 32, 161–171 (2020). https://doi.org/10.1007/s00161-019-00792-0

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