Abstract
The statistics of the nodal lines of scalar fields in two-dimensional (2d) turbulence is found to be conformal invariant and equivalent to that of cluster boundaries in critical phenomena. That allows for a rich variety of exact analytic results, first time in turbulence studies. In particular, the statistics of zero-vorticity lines in Navier-Stokes turbulence is found to be equivalent to that of critical percolation. The statistics of the zero-temperature lines in surface quasi-geostrophic (SQG) turbulence is found to be equivalent to that of the isolines of a Gaussian (free) field.
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