Experimental evidence of conformal invariance in soap film turbulent flows

TL;DR

This study provides experimental evidence that isocontours in soap film turbulence exhibit conformal invariance, aligning with Schramm-L"owner evolution, especially during inverse energy cascade development.

Contribution

It demonstrates conformal invariance in soap film turbulence through experimental visualization and analysis, linking physical flow features to theoretical SLE models.

Findings

Conformal invariance observed during inverse energy cascade.

Diffusivity close to 8/3 in conformal invariance cases.

No conformal invariance detected when cascade is weak.

Abstract

We present experimental evidence of statistical conformal invariance in isocontours of fluid thickness in experiments of two-dimensional turbulence using soap films. A Schlieren technique is used to visualize regions of the flow with constant film thickness, and association of isocontours with Schramm-L\"owner evolution (SLE) is used to identify conformal invariance. In experiments where an inverse energy cascade develops, statistical evidence is consistent with such an association. The diffusivity of the associated one-dimensional Brownian process is close to 8/3, a value previously identified in isocontours of vorticity in high-resolution numerical simulations of two-dimensional turbulence (D. Bernard et al., Nature Phys. 2, 124, 2006). In experiments where the inverse energy cascade is not sufficiently developed, no statistical evidence of conformal invariance is found.