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Relativistic hydrodynamics represents a powerful tool to investigate the time evolution of the strongly interacting quark gluon plasma created in ultrarelativistic heavy ion collisions. The equations are solved often numerically, and numerous analytic solutions also exist. However, the inclusion of viscous effects in exact, analytic solutions has received less attention. Here we utilize Hubble flow to investigate the role of bulk viscosity, and present different classes of exact, analytic solutions valid also in the presence of dissipative effects.
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The solutions of relativistic viscous hydrodynamics for longitudinal expanding fireballs is investigated with the Navier-Stokes theory and Israel-Stewart theory. The energy and Euler conservation equations for the viscous fluid are derived in Rindler coordinates with the longitudinal expansion effect is small. Under the perturbation assumption, an analytical perturbation solution for the Navier-Stokes approximation and numerical solutions for the Israel-Stewart approximation are presented. The temperature evolution with both shear viscous effect and longitudinal acceleration effect in the longitudinal expanding framework are presented and specifically temperature profile shows symmetry Gaussian shape in the Rindler coordinates. In addition, in the presence of the longitudinal acceleration expanding effect, the results of the Israel-Stewart approximation are compared to the results from Bjorken and Navier-Stokes approximation, and it gives a good description than the Navier-Stokes theories results at the early stages of evolution.
Hydrodynamics is a general theoretical framework for describing the long-time large-distance behaviors of various macroscopic physical systems, with its equations based on conservation laws such as energy-momentum conservation and charge conservation. Recently there has been significant interest in understanding the implications of angular momentum conservation for a corresponding hydrodynamic theory. In this work, we examine the key conceptual issues for such a theory in the relativistic regime where the orbital and spin components get entangled. We derive the equations for relativistic viscous hydrodynamics with angular momentum through Navier-Stokes type of gradient expansion analysis.
The second-order hydrodynamic equations for evolution of shear and bulk viscous pressure have been derived within the framework of covariant kinetic theory based on the effective fugacity quasiparticle model. The temperature-dependent fugacity parameter in the equilibrium distribution function leads to a mean field term in the Boltzmann equation which affects the interactions in the hot QCD matter. The viscous corrections to distribution function, up to second-order in gradient expansion, have been obtained by employing a Chapman-Enskog like iterative solution of the effective Boltzmann equation within the relaxation time approximation. The effect of mean field contributions to transport coefficients as well as entropy current has been studied up to second-order in gradients. In contrast to the previous calculations, we find non-vanishing entropy flux at second order. The effective description of relativistic second-order viscous hydrodynamics, for a system of interacting quarks and gluons, has been quantitatively analyzed in the case of the $1+1-$dimensional boost invariant longitudinal expansion. We study the proper time evolution of temperature, pressure anisotropy, and viscous corrections to entropy density for this simplified expansion. The second order evolution of quark-gluon plasma is seen to be affected significantly with the inclusion of mean field contributions and the realistic equation of state.
We propose to model the dissipative hydrodynamics used in description of the multiparticle production processes ($d$-hydrodynamics) by a special kind of the perfect nonextensive fluid ($q$-fluid) where $q$ denotes the nonextensivity parameter appearing in the nonextensive Tsallis statistics. The advantage of $q$-hydrodynamics lies in its formal simplicity in comparison to the $d$-hydrodynamics. We argue that parameter $q$ describes summarily (at least to some extent) all dynamical effects behind the viscous behavior of the hadronic fluid.
The stability and causality of the Landau-Lifshitz theory and the Israel-Stewart type causal dissipative hydrodynamics are discussed. We show that the problem of acausality and instability are correlated in relativistic dissipative hydrodynamics and instability is induced by acausality. We further discuss the stability of the scaling solution. The scaling solution of the causal dissipative hydrodynamics can be unstable against inhomogeneous perturbations.
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