Conformal invariance of weakly compressible two-dimensional turbulence

TL;DR

This paper investigates the conformal invariance of vorticity clusters in weakly compressible 2D turbulence, demonstrating scaling invariance and percolation-like statistics in the inverse cascade range through high-resolution simulations.

Contribution

It provides the first evidence of conformal invariance and percolation properties in weakly compressible 2D turbulence, extending previous incompressible turbulence results.

Findings

Scaling invariance of inverse cascade close to Kolmogorov prediction

Vorticity isolines exhibit critical percolation statistics

Conformal invariance observed in weakly compressible turbulence

Abstract

We study conformal invariance of vorticity clusters in weakly compressible two-dimensional turbulence at low Mach numbers. On the basis of very high resolution direct numerical simulation we demonstrate the scaling invariance of the inverse cascade with scaling close to Kolmogorov prediction. In this range of scales, the statistics of zero-vorticity isolines are found to be compatible with those of critical percolation, thus generalizing the results obtained in incompressible Navier-Stokes turbulence.