Possible Tests of Conformal Turbulence through Boundaries

TL;DR

This paper explores how boundary conditions in two-dimensional conformal turbulence influence measurable quantities, proposing experimental tests to verify conformal invariance effects in turbulent flows.

Contribution

It systematically analyzes boundary effects in 2D turbulence using conformal field theory, including boundary shape changes and operator insertions, and suggests experimental tests.

Findings

Boundary shape transformations affect energy spectra.

Boundary operators alter velocity profiles.

Moduli parameters influence one-point functions in turbulence.

Abstract

We investigate various boundary conditions in two dimensional turbulence systematically in the context of conformal field theory. Keeping the conformal invariance, we can either change the shape of boundaries through finite conformal transformations, or insert boundary operators so as to handle more general cases. Effects of such operations will be reflected in physically measurable quantities such as the energy power spectrum $E(k)$ or the average velocity profiles. We propose that these effects can be used as a possible test of conformal turbulence in an experimental setting. We also study the periodic boundary conditions, i.e. turbulence on a torus geometry. The dependence of moduli parameter $q$ appears explictly in the one point functions in the theory, which can also be tested.