Search for conformal invariance in compressible two-dimensional turbulence

TL;DR

This study investigates whether vorticity isolines in two-dimensional compressible turbulence exhibit conformal invariance as predicted by Schramm-L"owner Evolution, finding noticeable deviations from the theory.

Contribution

The paper applies SLE tests to vorticity isolines in compressible turbulence, providing the first such analysis in this context and revealing departures from conformal invariance.

Findings

Vorticity isolines show deviations from SLE predictions

Conformal invariance is not observed in the measured turbulence

Results suggest complexity beyond equilibrium critical systems

Abstract

We present a search for conformal invariance in vorticity isolines of two-dimensional compressible turbulence. The vorticity is measured by tracking the motion of particles that float at the surface of a turbulent tank of water. The three-dimensional turbulence in the tank has a Taylor microscale $Re_\lambda \simeq 160$. The conformal invariance theory being tested here is related to the behavior of equilibrium systems near a critical point. This theory is associated with the work of L\"owner, Schramm and others and is usually referred to as Schramm-L\"owner Evolution (SLE). The system was exposed to several tests of SLE. The results of these tests suggest that zero-vorticity isolines exhibit noticeable departures from this type of conformal invariance.