Dissipative hydrodynamics in2+1dimensions

Abstract

In $2+1$ dimensions, we simulated the hydrodynamic evolution of quark-gluon plasma (QGP) fluid with dissipation due to shear viscosity. Comparison of the evolution of ideal and viscous fluids, both initialized under the same conditions, e.g., same equilibration time, energy density and velocity profile, reveals that the dissipative fluid evolves slowly, cooling at a slower rate. Cooling slows even more at higher viscosities. The fluid velocities, however, evolve faster in a dissipative fluid than in an ideal fluid. The transverse expansion is also enhanced in dissipative evolution. For the same decoupling temperature, the freeze-out surface for a dissipative fluid is more extended than that for an ideal fluid. Dissipation produces entropy as a result of which particle production is increased. Particle production is increased as a result of the (i) the extension of the freeze-out surface and (ii) the change of the equilibrium distribution function to a nonequilibrium one, the latter effect being prominent at large transverse momentum. Compared to ideal fluid, transverse momentum distribution of pion production is considerably enhanced. Enhancement is greater at high ${p}_{T}$ than at low ${p}_{T}$. Pion production also increases with viscosity; the greater the viscosity, the greater the pion production. Dissipation also modifies the elliptic flow, which is reduced in viscous dynamics. Also, contrary to ideal dynamics where elliptic flow continues to increase with transverse momentum, in viscous dynamics elliptic flow tends to saturate at large transverse momentum. The analysis suggests that the initial conditions of the hot, dense matter produced in Au+Au collisions at the Relativistic Heavy Ion Collider (RHIC), as extracted from ideal fluid analysis, can be changed significantly if the QGP fluid is viscous.