Fluid turbulence and eddy viscosity in relativistic heavy-ion collisions

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.

Figures (1)

• Figure 1: Effective versus standard viscosity for $\bar{\lambda}=10^{-3}$. Decreasing $\eta/s$ from large values, the effective viscosity changes rapidly to extremely small values close to the critical viscosity $\eta/s=(\bar{\lambda})^{1/3}$. Decreasing $\eta/s$ further may even result in negative effective viscosity. However, at this point the calculation breaks down and the result cannot be trusted.