Double Solutions of the Euler and Navier-Stokes Equations Process of Origination the Vorticity and Turbulence

L. I. Petrova

doi:doi:10.11648/j.fm.20170302.11

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Double Solutions of the Euler and Navier-Stokes Equations Process of Origination the Vorticity and Turbulence

L. I. Petrova

Published in Fluid Mechanics (Volume 3, Issue 2)

Received: 29 October 2016 Accepted: 2 December 2016 Published: 21 March 2017

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Abstract

The Euler and Navier-Stokes equations, which describe flow of fluids and gases, possess solutions of two types, namely, the solutions that are not functions (they depends not only on the variables) and the solutions that are discrete functions. The solutions of the first type describe a non-equilibrium state of a gas dynamic system. And the solutions of the second type describe a locally-equilibrium state of a gas dynamic system. The transition from the solutions of the first type to ones of the second type describe a transition of gas dynamic system from a non-equilibrium state to a locally-equilibrium state, and this process is accompanied by emergence of vorticity or turbulence.

Published in	Fluid Mechanics (Volume 3, Issue 2)
DOI	10.11648/j.fm.20170302.11
Page(s)	6-12
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Skew-Symmetric Forms, Solutions of Two Types, Non-equilibrium State and Locally-Equilibrium, Emergence of Vorticity or Turbulence

References

[1]	Petrova L. I., Role of skew-symmetric differential forms in mathematics, (2010), http://arxiv.org/pdf/1007.4757vl.pdf.
[2]	Clark J. F., Machesney M., “The Dynamics of Real Gases”, Butterworths, London, 1964.
[3]	Haywood R. W., “Equilibrium Thermodynamics”, Wiley Inc. 1980.
[4]	Petrova L. I., Relationships between discontinuities of derivatives on characteristics and trajectorie., J. Computational Mathematics and Modeling, Vol. 20, N. 4, 2009, pp. 367-372.
[5]	Glansdorff P., Prigogine I. “Thermodynamic Theory of Structure, Stability and Fluctuations”, Wiley, N. Y., 1971.
[6]	Petrova L. I., Exterior and evolutionary differential forms in mathematical physics: Theory and Applications, -Lulu.com, (2008), 157.
[7]	Petrova L. I., The mechanism of generation of physical structures. // Nonlinear Acoustics - Fundamentals and Applications (18th International Symposium on Nonlinear Acoustics, Stockholm, Sweden, 2008) - New York, American Institute of Physics (AIP), 2008, pp. 151-154.
[8]	Petrova L. I., Integrability and the properties of solutions to Euler and Navier-Stokes equations, Journal of Mathematics Research, Vol. 4, No. 3, (2012), 19-28.
[9]	Petrova L., The Peculiarity of Numerical Solving the Euler and Navier-Stokes Equations, American Journal of Computational Mathematics, Vol. 4, No. 4, (2014), 305-310.
[10]	Petrova L. I. The noncommutativity of the conservation laws: Mechanism of origination of vorticity and turbulence, International Journal of Theoretical and Mathematical Physics, Vol. 2, No.4, 2012, pp. 84-90.

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L. I. Petrova. (2017). Double Solutions of the Euler and Navier-Stokes Equations Process of Origination the Vorticity and Turbulence. Fluid Mechanics, 3(2), 6-12. https://doi.org/10.11648/j.fm.20170302.11

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ACS Style

L. I. Petrova. Double Solutions of the Euler and Navier-Stokes Equations Process of Origination the Vorticity and Turbulence. Fluid Mech. 2017, 3(2), 6-12. doi: 10.11648/j.fm.20170302.11

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AMA Style

L. I. Petrova. Double Solutions of the Euler and Navier-Stokes Equations Process of Origination the Vorticity and Turbulence. Fluid Mech. 2017;3(2):6-12. doi: 10.11648/j.fm.20170302.11

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@article{10.11648/j.fm.20170302.11,
  author = {L. I. Petrova},
  title = {Double Solutions of the Euler and Navier-Stokes Equations Process of Origination the Vorticity and Turbulence},
  journal = {Fluid Mechanics},
  volume = {3},
  number = {2},
  pages = {6-12},
  doi = {10.11648/j.fm.20170302.11},
  url = {https://doi.org/10.11648/j.fm.20170302.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.fm.20170302.11},
  abstract = {The Euler and Navier-Stokes equations, which describe flow of fluids and gases, possess solutions of two types, namely, the solutions that are not functions (they depends not only on the variables) and the solutions that are discrete functions. The solutions of the first type describe a non-equilibrium state of a gas dynamic system. And the solutions of the second type describe a locally-equilibrium state of a gas dynamic system. The transition from the solutions of the first type to ones of the second type describe a transition of gas dynamic system from a non-equilibrium state to a locally-equilibrium state, and this process is accompanied by emergence of vorticity or turbulence.},
 year = {2017}
}

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TY  - JOUR
T1  - Double Solutions of the Euler and Navier-Stokes Equations Process of Origination the Vorticity and Turbulence
AU  - L. I. Petrova
Y1  - 2017/03/21
PY  - 2017
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AB  - The Euler and Navier-Stokes equations, which describe flow of fluids and gases, possess solutions of two types, namely, the solutions that are not functions (they depends not only on the variables) and the solutions that are discrete functions. The solutions of the first type describe a non-equilibrium state of a gas dynamic system. And the solutions of the second type describe a locally-equilibrium state of a gas dynamic system. The transition from the solutions of the first type to ones of the second type describe a transition of gas dynamic system from a non-equilibrium state to a locally-equilibrium state, and this process is accompanied by emergence of vorticity or turbulence.
VL  - 3
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Author Information

L. I. Petrova

Moscow State University, Department of Computational Mathematics and Cybernetics, Moscow, Russia

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APA Style

L. I. Petrova. (2017). Double Solutions of the Euler and Navier-Stokes Equations Process of Origination the Vorticity and Turbulence. Fluid Mechanics, 3(2), 6-12. https://doi.org/10.11648/j.fm.20170302.11

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ACS Style

L. I. Petrova. Double Solutions of the Euler and Navier-Stokes Equations Process of Origination the Vorticity and Turbulence. Fluid Mech. 2017, 3(2), 6-12. doi: 10.11648/j.fm.20170302.11

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AMA Style

L. I. Petrova. Double Solutions of the Euler and Navier-Stokes Equations Process of Origination the Vorticity and Turbulence. Fluid Mech. 2017;3(2):6-12. doi: 10.11648/j.fm.20170302.11

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@article{10.11648/j.fm.20170302.11,
  author = {L. I. Petrova},
  title = {Double Solutions of the Euler and Navier-Stokes Equations Process of Origination the Vorticity and Turbulence},
  journal = {Fluid Mechanics},
  volume = {3},
  number = {2},
  pages = {6-12},
  doi = {10.11648/j.fm.20170302.11},
  url = {https://doi.org/10.11648/j.fm.20170302.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.fm.20170302.11},
  abstract = {The Euler and Navier-Stokes equations, which describe flow of fluids and gases, possess solutions of two types, namely, the solutions that are not functions (they depends not only on the variables) and the solutions that are discrete functions. The solutions of the first type describe a non-equilibrium state of a gas dynamic system. And the solutions of the second type describe a locally-equilibrium state of a gas dynamic system. The transition from the solutions of the first type to ones of the second type describe a transition of gas dynamic system from a non-equilibrium state to a locally-equilibrium state, and this process is accompanied by emergence of vorticity or turbulence.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Double Solutions of the Euler and Navier-Stokes Equations Process of Origination the Vorticity and Turbulence
AU  - L. I. Petrova
Y1  - 2017/03/21
PY  - 2017
N1  - https://doi.org/10.11648/j.fm.20170302.11
DO  - 10.11648/j.fm.20170302.11
T2  - Fluid Mechanics
JF  - Fluid Mechanics
JO  - Fluid Mechanics
SP  - 6
EP  - 12
PB  - Science Publishing Group
SN  - 2575-1816
UR  - https://doi.org/10.11648/j.fm.20170302.11
AB  - The Euler and Navier-Stokes equations, which describe flow of fluids and gases, possess solutions of two types, namely, the solutions that are not functions (they depends not only on the variables) and the solutions that are discrete functions. The solutions of the first type describe a non-equilibrium state of a gas dynamic system. And the solutions of the second type describe a locally-equilibrium state of a gas dynamic system. The transition from the solutions of the first type to ones of the second type describe a transition of gas dynamic system from a non-equilibrium state to a locally-equilibrium state, and this process is accompanied by emergence of vorticity or turbulence.
VL  - 3
IS  - 2
ER  -

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