Exact Scaling Relations In Relativistic Hydrodynamic Turbulence

TL;DR

This paper derives exact scaling relations for relativistic hydrodynamic turbulence, generalizing known non-relativistic results and challenging traditional energy cascade interpretations, with implications for experiments.

Contribution

It introduces a general relation for current-density correlations that leads to exact scaling laws in relativistic turbulence, extending classical turbulence theory.

Findings

Derived exact scaling relations for relativistic turbulence.

Showed relations reduce to Kolmogorov in slow motion limit.

Challenged traditional energy cascade interpretation.

Abstract

We consider the steady state statistics of turbulence in general classes of dissipative hydrodynamic equations, where the fluctuations are sustained by a random source concentrated at large scales. It is well known that in some particular cases, such as non-relativistic incompressible turbulence, a Kolmogorov-type exact scaling relation for a correlation function holds. We show that all such scaling relations follow from a general relation on the current-density correlation function. The derivation does not require an energy cascade picture and suggests that this traditional interpretation of the Kolmogorov relation for incompressible turbulence may be misleading. Using this we derive exact scaling results for compressible turbulence in relativistic hydrodynamics, which reduce in the slow motion limit to the Kolmogorov relation. We discuss the experimental implications of the results.