On Scale Versus Conformal Symmetry in Turbulence

Abstract

We consider the statistical description of steady state fully developed incompressible fluid turbulence at the inertial range of scales in any number of spatial dimensions. We show that turbulence statistics is scale but not conformally covariant, with the only possible exception being the direct enstrophy cascade in two space dimensions. We argue that the same conclusions hold for compressible non-relativistic turbulence as well as for relativistic turbulence. We discuss the modification of our conclusions in the presence of vacuum expectation values of negative dimension operators. We consider the issue of non-locality of the stress-energy tensor of inertial range turbulence field theory.

4 pages, revtex, ref. added. We discuss the modification of our conclusions in the presence of vacuum expectation values of negative dimension operators

References in corpus (4)

• Emergence of Multi-Scaling in a Random Force-Stirred Fluid
• Spontaneous Symmetry Breaking, Conformal Anomaly and Incompressible Fluid Turbulence
• Numerical Measurements of Scaling Relations in Two-Dimensional Conformal Fluid Turbulence
• Scaling Relations in Two-Dimensional Relativistic Hydrodynamic Turbulence

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• Scale without Conformal Invariance in bottom-up Holography