Fluid turbulence and eddy viscosity in relativistic heavy-ion collisions

TL;DR

This paper derives the eddy viscosity in relativistic turbulent fluids, showing it can be negative in two dimensions, potentially explaining the low viscosity observed in heavy-ion collisions and affecting flow measurements.

Contribution

It provides a theoretical derivation of eddy viscosity in relativistic fluids, highlighting its negative value in two dimensions relevant to heavy-ion collisions.

Findings

Eddy viscosity in shear mode is the same as for incompressible fluids.

In two dimensions, eddy viscosity is negative, reducing effective viscosity.

Potential explanation for low viscosity observed at RHIC.

Abstract

The eddy viscosity for a turbulent compressible fluid with a relativistic equation of state is derived. Compressibility allows for sound modes, but the eddy viscosity in the shear mode is found to be the same as for incompressible fluids. For two space dimensions (which is the relevant case for the dynamics of relativistic heavy-ion collisions) the eddy viscosity in the shear mode is negative, reducing the effective viscosity below its microscopic value. This could explain the tiny viscosity found at RHIC. Implications for the experimentally accessible elliptic flow coefficient at the LHC are speculated on.