Viscosity and Thermalization

I solve the Relativistic Navier Stokes Equations assuming boost invariance and rotational symmetry. I compare the resulting numerical solutions for two limiting models of the shear viscosity. In the first model the shear viscosity is made proportional to the temperature. Thus, $\eta \propto T/\sigma_0$ where $\sigma_0$ is some fixed cross section (perhaps $\sigma_0 \sim \Lambda_{QCD}^{-2}$) . This viscosity model is typical of the classical Boltzmann simulations of Gyulassy and Molnar. In the second model the shear viscosity is made proportional to $T^3$. This model is typical of high temperature QCD. When the initial mean free path of the $T^3$ model is four times larger than the $T/\sigma_0$ model, the two models of viscosity produce the same radial flow. This result can be understood with simple scaling arguments. Thus, the large transport opacity needed in classical Boltzmann simulations is in part an artifact of the fixed scale $\sigma_0$ in these models.