Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Transition between spiral and target states in Rayleigh–Bénard convection

Abstract

RAYLEIGH–BÉNARD convection1–4, which occurs when a shallow fluid layer is heated from below, is commonly regarded as a paradigm for pattern formation under non-equilibrium conditions. The formation of hexagonal arrays of Bénard cells is well known, but more complex patterns such as targets5 and spirals5–11 have also been reported. Similar patterns have been seen in electrohydrodynamical convection12,13, oscillatory chemical reactions14–19 and biological systems19,20. In general, the spiral and target states are found for different experimental conditions. Here we report the observation of a continuous transition between states containing many spirals and many targets, in a fluid undergoing Rayleigh–Bénard convection near the gas–liquid critical point. Whether spirals or targets are observed depends on the Prandtl number, the ratio between the thermal and viscous timescales in the fluid. Neither of these states seems to be predicted by the hydrodynamic equations that describe the fluid motions1–4, 21. The fact that the transformation of one pattern into the other is continuous, and that under some conditions they can coexist, suggests that they may be generated by the same or a similar mechanism.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Prices may be subject to local taxes which are calculated during checkout

Similar content being viewed by others

References

  1. Manneville, P. Dissipative Structures and Weak Turbulence (Academic, Boston, 1990).

    MATH  Google Scholar 

  2. Normand, C., Pomeau, Y. & Verlade, M. G. Rev. Mod. Phys. 49, 581–624 (1977).

    Article  ADS  Google Scholar 

  3. Busse, F. H. Rep. Prog. Phys. 41, 1929–1967 (1978).

    Article  ADS  Google Scholar 

  4. Bergé, P. & Dubois, M. Contemp. Phys. 25, 535–582 (1984).

    Article  ADS  Google Scholar 

  5. Assenheimer, M. & Steinberg, V. Phys. Rev. Lett. 70, 3888–3891 (1993).

    Article  ADS  CAS  Google Scholar 

  6. Bodenschatz, E., de Bruyn, J. R., Ahlers, G. & Cannell, D. S. Phys. Rev. Lett. 67, 3078–3081 (1991).

    Article  ADS  CAS  Google Scholar 

  7. Bodenschatz, E. et al. Physica D61, 77–93 (1992).

    Google Scholar 

  8. Morris, S. W., Bodenschatz, E., Cannell, D. S. & Ahlers, G. Phys. Rev. Lett. 71, 2026–2029 (1993).

    Article  ADS  CAS  Google Scholar 

  9. Xi, H. W., Vinals, J. & Gunton, J. D. Phys. Rev. A46, R4483–R4486 (1992).

    Article  ADS  CAS  Google Scholar 

  10. Xi, H. W., Gunton, J. D. & Viñals, J. Phys. Rev. E47 R2987–R2990 (1993).

    Article  ADS  CAS  Google Scholar 

  11. Xi, H. W., Gunton, J. D. & Viñals, J. Phys. Rev. Lett. 71, 2030–2033 (1993).

    Article  ADS  CAS  Google Scholar 

  12. Sano, M., Sato, K., Nasuno, S. & Kokubo, H. Phys. Rev. A46, 3540–3545 (1992).

    Article  ADS  CAS  Google Scholar 

  13. Janiaud, B., Kokubo, H. & Sano, M., Phys. Rev. E47 R2237–R2240 (1993).

    ADS  CAS  Google Scholar 

  14. Müller, S. C., Plesser, T. & Hess, B. Science 230, 661–663 (1985).

    Article  ADS  Google Scholar 

  15. Madore, B. F. & Freedman, W. L. Am. Sci. 75, 252–259 (1987).

    ADS  Google Scholar 

  16. Kessler, D. A. & Levine, H. Physica D39 1–14 (1989).

    MathSciNet  CAS  Google Scholar 

  17. Markus, M. & Hess, B. Nature 347, 56–58 (1990).

    Article  ADS  CAS  Google Scholar 

  18. Skinner, G. S. & Swinney, H. L. Physica D48 1–16 (1991).

    CAS  Google Scholar 

  19. Tyson, J. J. & Keener, J. P. Physica D32, 327–361 (1988).

    MathSciNet  Google Scholar 

  20. Newell, P. C. & Ross, F. M. J. gen. Microbiol. 128, 2715–2724 (1982).

    CAS  Google Scholar 

  21. Busse, F. H. J. fluid Mech. 30, 625–649 (1967).

    Article  ADS  Google Scholar 

  22. Morsy, T. E. J. chem. engng Data 15, 256–265 (1970).

    Article  CAS  Google Scholar 

  23. Ciliberto, S., Pamploni, E. & Pérez-Garcia, C. Phys. Rev. Lett. 61, 1198–1201 (1988).

    Article  ADS  CAS  Google Scholar 

  24. Newell, A. C. & Passot, T. Phys. Rev. Lett. 68, 1846–1849 (1992).

    Article  ADS  CAS  Google Scholar 

  25. Siggia, E. D. & Zippelius, A. Phys. Rev. Lett. 47, 835–838 (1981).

    Article  ADS  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Assenheimer, M., Steinberg, V. Transition between spiral and target states in Rayleigh–Bénard convection. Nature 367, 345–347 (1994). https://doi.org/10.1038/367345a0

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/367345a0

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing