Conformal invariance in two-dimensional turbulence
By D. Bernard, Guido Boffetta, Antonio Celani, Gregory Falkovich. 2006
174 citations recorded by the source corpus.
The simplicity of fundamental physical laws manifests itself in fundamental symmetries. Although systems with an infinite number of strongly interacting degrees of freedom (in particle physics and critical phenomena) are hard to describe, they often demonstrate symmetries, in particular scale invariance. In two dimensions (2D) locality often extends scale invariance to a wider class of conformal transformations that allow non-uniform rescaling. Conformal invariance enables a thorough classification of universality classes of critical phenomena in 2D. Is there conformal invariance in 2D turbulence, a paradigmatic example of a strongly interacting non-equilibrium system? Here, we show numerically that some features of a 2D inverse turbulent cascade show conformal invariance. We observe that the statistics of vorticity clusters are remarkably close to that of critical percolation, one of the simplest universality classes of critical phenomena. These results represent a key step in the unification of 2D physics within the framework of conformal symmetry.
Subfields: Condensed Matter Physics, Global and Planetary Change, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/ac93f4073753670073b4c70e8cf22a3dcf2529a2
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Citations in the corpus
- Two-Dimensional Turbulence (2012, background): “On the basis of these numerical simulations at high resolution, Bernard et al. (2006) were able to observe the property of conformal invariance for vorticity isolines in the inverse cascade (see the sidebar, Conformal Invariance).”
- Recent advances in percolation theory and its applications (2015, background): “Among which, SLE could provide quite unexpected connections between some features of interacting systems and ordinary uncorrelated percolation [26, 90].”
- Statistical mechanics of two-dimensional and geophysical flows (2011, background): “Predictions of the self-similar cascade theory have been followed by numerous experimental studies in many different settings over the last three decades (see [8,9] and references therein), and this has led to beautiful experimental results [179,154].”