Skip to main content
SpringerLink
Log in

Fixed point limit behavior ofN-mode truncated Navier-Stokes equations asN increases

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

Abstract

The fixed point behavior ofN-mode truncations of the Navier-Stokes equations on a two-dimensional torus is investigated asN increases. FromN=44 on the behavior does not undergo any qualitative change. Furthermore, the bifurcations occur at critical parameter values which clearly tend to stabilize asN approaches 100.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. E. N. Lorenz, Deterministic nonperiod flow,J. Atmos. Sci. 20:130 (1963).

    Google Scholar 

  2. J. H. Curry, A generalized Lorenz system,Commun. Math. Phys. 60:193 (1978).

    Google Scholar 

  3. H. Yahata, Temporal development of the Taylor vortices in a rotating fluid. V,Prog. Theor. Phys. 69:396 (1983).

    Google Scholar 

  4. S. A. Orszag and L. C. Kells, Transition to turbulence in plane Poiseuille and plane Couette flow,J. Fluid Mech. 96:159 (1980).

    Google Scholar 

  5. M. E. Brachet, D. I. Meiron, S. A. Orszag, B. G. Nickel, R. H. Morf, and U. Frisch, Small-scale structure of the Taylor-Green vortex,J. Fluid Mech. 130:411 (1983).

    Google Scholar 

  6. C. Boldrighini and V. Franceschini, A five-dimensional truncation of the plane incompressible Navier-Stokes solution,Commun. Math. Phys. 64:159 (1979).

    Google Scholar 

  7. V. Franceschini and C. Tebaldi, A seven-mode truncation of the plane incompressible Navier-Stokes equations,J. Stat. Phys. 25:397 (1981).

    Google Scholar 

  8. G. Riela, A new six-mode truncation of the Navier-Stokes equations on a twodimensional torus: A numerical study,II Nuovo Cimento 69B:245 (1982).

    Google Scholar 

  9. V. Franceschini, Two models of truncated Navier-Stokes equations on a two-dimension torus,Phys. Fluids 26:433 (1983).

    Google Scholar 

  10. V. Franceschini and C. Tebaldi, to be published.

  11. G. Riela, University of Palermo, preprint.

  12. C. Foias, O. P. Manley, R. Teman, and Y. M. Treve, Number of modes governing two-dimensional viscous, incompressible flows,Phys. Rev. Lett. 50:1031 (1983).

    Google Scholar 

  13. V. Franceschini, Truncated Navier-Stokes equations on a two-dimensional torus, inCoupled Nonlinear Oscillators, J. Chandra and A. C. Scott, eds. (North-Holland, Amsterdam, 1983).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Universita' di Modena, via Campi 213B, 41100, Modena, Italy

    Valter Franceschini & Fernando Zironi

  2. Dipartimento di Matematica, Universita' di Bologna, via Vallescura 2, 40126, Bologna, Italy

    Claudio Tebaldi

Authors
  1. Valter Franceschini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Claudio Tebaldi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fernando Zironi
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Franceschini, V., Tebaldi, C. & Zironi, F. Fixed point limit behavior ofN-mode truncated Navier-Stokes equations asN increases. J Stat Phys 35, 387–397 (1984). https://doi.org/10.1007/BF01014392

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01014392

Key words

Search

Navigation