Skip to main content

Thank you for visiting 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.


The power of two dimensions

Certain aspects of two-dimensional turbulence are remarkably similar to those found in critical percolation, and show conformal invariance. But there is both less, and more, to this observation than meets the eye.

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

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: An example of critical percolation.


  1. Bernard, D., Boffetta, G., Celani, A. & Falkovich, G. Nature Phys. 2, 124–128 (2006).

    Article  ADS  Google Scholar 

  2. Kolmogorov, A. N. Dokl. Akad. Nauk SSSR 30, 9–13 (1941); reprinted in Proc. R. Soc. Lond. A 434, 9–13 (1991).

    Google Scholar 

  3. Kraichnan, R. H. Phys. Fluids 10, 1417–1423 (1967).

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations


Rights and permissions

Reprints and Permissions

About this article

Cite this article

Cardy, J. The power of two dimensions. Nature Phys 2, 67–68 (2006).

Download citation

  • Issue Date:

  • DOI:


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