Conformal invariance and 2D turbulence

Gregory Falkovich, Weizmann Institute

I shall review remarkable data on the statistics of vorticity isolines in 2d turbulence described by the Euler equation and related models. The data suggest that the isolines belong to the class of random curves called Schramm–Loewner Evolution. The statistics is conformally invariant. I shall briefly discuss direct relations between isolines in turbulence and cluster boundaries in critical phenomena. In particular, nodal lines of vorticity seem to be equivalent to critical percolation line. At the end, possible integrability of 2d Euler equation is discussed.

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