Skip to main content
Log in

Macrodynamics: Large-scale structures in turbulent media

  • Articles
  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

We develop a method to derive the macroscopic equations governing the evolution of the mean field in continuous turbulent media. The approach is based on the concept of local equilibrium, which enables one to evaluate averages of nonlinear terms and to close the averaged equation. Examples include the Kuramoto-Sivashinsky equation and its modifications.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. G. I. Sivashinsky and D. M. Michelson, On irregular wave flow of a liquid film down a vertical plane,Prog. Theor. Phys. 63:2112–2114 (1980).

    Google Scholar 

  2. J. M. Hyman, B. Nicolaenko, and S. Zalesky, Order and complexity in the Kuramoto-Sivashinsky model of weakly turbulent interfaces,Physica D 23:265–292 (1986).

    Google Scholar 

  3. A. S. Monin,The Solar Cycle (St. Petersburg, 1980).

  4. U. Frish and S. A. Orszag, Turbulence: Challenges for theory and experiment,Phys. Today 1990 (January):24–32.

  5. U. Frish, B. Hasslacher, and Y. Pomeau, Lattice-gas automata for Navier-Stokes equations,Phys. Rev. Lett. 56:1505–1508 (1986).

    Google Scholar 

  6. J. L. Lebowitz, E. Presutti, and H. Spohn, Microscopic models of hydrodynamic behavior,J. Stat. Phys. 51:841–862 (1986).

    Google Scholar 

  7. J. L. Lebowitz, E. Orlandi, and E. Presutti, Convergence of stochastic cellular automaton to Burgers' equation: Fluctuations and stability,Physica D 33:165–188 (1988).

    Google Scholar 

  8. Y. Kuramoto and I. Nishikawa, Statistical macrodynamics of large dynamical systems. Case of a phase transition in oscillator communities,J. Stat. Phys. 49:569–605 (1987).

    Google Scholar 

  9. S. V. Ershov, Chaotic attractors in the delay-differential equation: High-dimensional approximation, IAM preprint 94 (1988) [in Russian]; Asymptotic theory of multi-dimensional chaos,J. Stat. Phys., this issue.

  10. C. Maes and S. B. Shlosmann, Ergodicity of cellular automata: A constructive approach,Commun. Math. Phys. 135:233–251 (1991).

    Google Scholar 

  11. V. Yakhot, Large-scale properties of unstable systems governed by Kuramoto-Sivashinsky equation,Phys. Rev. A 24:642–644 (1981).

    Google Scholar 

  12. S. Zalesky, A stochastic model for the large-scale dynamics of some fluctuating interfaces,Physica 34D:427–38 (1989).

    Google Scholar 

  13. B. Shraiman, Order, disorder and phase turbulence,Phys. Rev. Lett. 37:325–328 (1986).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ershov, S.V., Potapov, A.B. Macrodynamics: Large-scale structures in turbulent media. J Stat Phys 69, 763–779 (1992). https://doi.org/10.1007/BF01050433

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01050433

Key words

Navigation