Skip to main content

Comparison of three-dimensional and two-dimensional statistical mechanics of shear layers for flow between two parallel plates

Abstract

It is shown that the averaged velocity profiles predicted by statistical mechanics of point vortices and statistical mechanics of vortex lines are practically indistinguishable for a shear flow between two parallel walls.

References

  1. Akulenko L., Nesterov S.: High-precision Methods in Eigenvalue, Problems and Their Applications. Chapman & Hall/CRC, Boca Raton (2005)

    MATH  Google Scholar 

  2. Berdichevsky V.: Thermodynamics of Chaos and Order. Addison-Wesly-Longman, London (1997)

    MATH  Google Scholar 

  3. Berdichevsky V.: Statistical mechanics of vortex lines. Phys. Rev. E. 57, 2885 (1998)

    MathSciNet  ADS  Article  Google Scholar 

  4. Berdichevsky V.: On statistical mechanics of vortex lines. Int. J. Eng. Sci. 40, 123 (2002)

    MATH  Article  Google Scholar 

  5. Berdichevsky V.: Averaged equations of ideal fluid turbulence. Continuum Mech. Thermodyn. 19, 133 (2007)

    MathSciNet  MATH  Article  Google Scholar 

  6. Lions P.-L., Majda A.: Equilibrium statistical theory for nearly parallel vortex filaments. Commun. Pure Appl. Math. 53, 76 (2000)

    MathSciNet  MATH  Article  Google Scholar 

  7. Montgomery D., Joyce G.: Negative temperature states for 2-dimensional guiding-center plasma. J. Plasma Phys. 10, 107 (1973)

    ADS  Article  Google Scholar 

  8. Montgomery D., Joyce G.: Statistical mechanics of “negative temperature” states. Phys. Fluids 17, 1139 (1974)

    MathSciNet  ADS  Article  Google Scholar 

  9. Pryce J.: Numerical Solution of Sturm–Liouville Problems. Oxford University Press, New York (1994)

    Google Scholar 

  10. Shirkov, L., Berdichevsky, V.: Izvestiya Vuzov. Severo-Kavkazkii Region, Special Issue Actual problems of mathematical hydrodynamics (2009)

Download references

Open Access

This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to L. Shirkov.

Additional information

Communicated by Samuel Forest.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

Shirkov, L., Berdichevsky, V. Comparison of three-dimensional and two-dimensional statistical mechanics of shear layers for flow between two parallel plates. Continuum Mech. Thermodyn. 25, 269–272 (2013). https://doi.org/10.1007/s00161-012-0249-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00161-012-0249-6

Keywords

  • Vortex dynamics
  • Hamiltonian systems
  • Turbulence
  • Boundary layer