Conformal Invariance in Water-Wave Turbulence

Area of Science:

• Fluid Dynamics
• Statistical Physics
• Conformal Field Theory

Background:

• Gravity wave turbulence is a complex phenomenon with potential connections to fundamental symmetries.
• Conformal invariant curves are theoretical constructs with applications in various physical systems.

Purpose of the Study:

• To experimentally investigate the statistical properties of zero-height isolines in gravity wave turbulence.
• To determine if these isolines can be described by conformal invariant curves, specifically stochastic Schramm-Löwner evolution (SLE).

Main Methods:

• Experimental investigation of gravity wave turbulence.
• Statistical analysis of zero-height isoline configurations.
• Comparison of experimental data with theoretical predictions of SLE.

Main Results:

• Direct evidence supporting the description of zero-height isolines by SLE.
• Determination of the diffusivity parameter κ = 2.88(8) for SLE.
• Observation that increased nonlinearity in height fields destroys conformal symmetry.

Conclusions:

• Zero-height isolines in gravity wave turbulence are physical realizations of conformal invariant curves.
• The findings provide a new link between fluid turbulence and concepts from conformal field theory.
• Scale invariance is maintained even when conformal symmetry is broken by nonlinearity.