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Stochastic Navier-Stokes Equation for a Compressible Fluid: Two-Loop Approximation

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11th Chaotic Modeling and Simulation International Conference (CHAOS 2018)

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Abstract

A model of fully developed turbulence of a compressible fluid is briefly reviewed. It is assumed that fluid dynamics is governed by a stochastic version of Navier-Stokes equation. We show how corresponding field theoretic-model can be obtained and further analyzed by means of the perturbative renormalization group. Two fixed points of the RG equations are found. The perturbation theory is constructed within formal expansion scheme in parameter y, which describes scaling behavior of random force fluctuations. Actual calculations for fixed points’ coordinates are performed to two-loop order.

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Acknowledgements

The work was supported by VEGA grant No. 1/0345/17 of the Ministry of Education, Science, Research and Sport of the Slovak Republic, and by the Russian Foundation for Basic Research within the Project No. 16-32-00086. N. M. G. acknowledges the support from the Saint Petersburg Committee of Science and High School.

Author information

Authors and Affiliations

  1. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980, Dubna, Russian Federation

    Michal Hnatič & Lukáš Mižišin

  2. Institute of Experimental Physics, Slovak Academy of Sciences, Watsonova 47, 040 01, Košice, Slovakia

    Michal Hnatič & Lukáš Mižišin

  3. Faculty of Sciences, Šafarik University, Moyzesova 16, 040 01, Košice, Slovakia

    Michal Hnatič & Tomáš Lučivjanský

  4. Department of Physics, Saint-Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg, 199034, Russian Federation

    Nikolay M. Gulitskiy

  5. School of Physics and Astronomy, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK

    Viktor Škultéty

Authors
  1. Michal Hnatič
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  2. Nikolay M. Gulitskiy
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  3. Tomáš Lučivjanský
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  4. Lukáš Mižišin
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Correspondence to Tomáš Lučivjanský .

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Editors and Affiliations

  1. ManLab, Technical University of Crete, Chania, Crete, Greece

    Christos H. Skiadas

  2. Complex Systems Modeling Laboratory, The University of Aizu, Aizuwakamatsu, Fukushima, Japan

    Ihor Lubashevsky

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Hnatič, M., Gulitskiy, N.M., Lučivjanský, T., Mižišin, L., Škultéty, V. (2019). Stochastic Navier-Stokes Equation for a Compressible Fluid: Two-Loop Approximation. In: Skiadas, C., Lubashevsky, I. (eds) 11th Chaotic Modeling and Simulation International Conference. CHAOS 2018. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-030-15297-0_16

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