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Using second--order dissipative hydrodynamics coupled self-consistently tothe linear $\sigma$ model we study the 2+1 dimensional evolution of thefireball created in Au+Au relativistic collisions. We analyze the influence ofthe dynamics of the chiral fields on the charged-hadron elliptic flow $v_2$ andon the ratio $v_4/(v_2)^2$ for a temperature-independent as well as for atemperature-dependent viscosity-to-entropy ratio $\eta/s$ calculated from thelinearized Boltzmann equation in the relaxation time approximation. We findthat $v_2$ is not very sensitive to the coupling of chiral sources to thehydrodynamic evolution, but the temperature dependence of $\eta/s$ plays a muchbigger role on this observable. On the other hand, the ratio $v_4/(v_2)^2$turns out to be much more sensitive than $v_2$ to both the coupling of thechiral sources and the temperature dependence of $\eta/s$.

Dissipative hydrodynamics coupled to chiral fields