Vorticity development is studied in the reaction plane of peripheral relativistic heavy-ion reactions where the initial state has substantial angular momentum. The earlier predicted rotation effect and Kelvin Helmholtz instability lead to significant initial vorticity and circulation. In low-viscosity quark gluon plasma this vorticity remains still significant at the time of freeze-out of the system, even if damping due to explosive expansion and dissipation decreases the vorticity and circulation. In the reaction plane the vorticity arises from the initial angular momentum, and it is stronger than in the transverse plane, where vorticity is caused by random fluctuations only.

With a Yang-Mills flux-tube initial state and a high-resolution (3+1)D particle-in-cell relativistic (PICR) hydrodynamics simulation, we calculate the polarization for different energies. The origination of polarization in high energy collisions is discussed, and we find linear impact parameter dependence of the global polarization. Furthermore, the global polarization in our model decreases very quickly in the low energy domain, and the decline curve fits well the recent results of Beam Energy Scan (BES) program launched by the STAR Collaboration at the Relativistic Heavy Ion Collider (RHIC). The time evolution of polarization is also discussed.

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We study an exact and extended solution of the fluid dynamical model of heavy ion reactions and estimate the rate of slowing down of the rotation due to the longitudinal and transverse expansion of the system. The initial state parameters of the model are set on the basis of a realistic (3 + 1)-dimensional fluid dynamical calculation at TeV energies, where the rotation is enhanced by the buildup of the Kelvin-Helmholtz instability in the flow.

The flow vorticity development is studied in the reaction plane of peripheral relativistic heavy-ion reactions at energies just above the threshold of the transition to a quark-gluon plasma (QGP). Earlier calculations at higher energies with larger initial angular momentum predicted significant vorticity leading to measurable polarization. Here we discuss the possibility of vorticity and circulation in dense plasma at lower temperatures. In low-viscosity QGP this vorticity still remains significant. Fluid dynamical processes in heavy-ion reactions were studied for a long time [1][2][3], and their use is becoming more dominant in recent years. With the quark-gluon plasma (QGP) production in these reactions, the scope of the fluid dynamical studies is widening at the same time [4]. As in the present studies, both different fluctuating modes and global collective processes lead to flow observables, so it becomes important to separate or split the two types of flow processes from each other [5,6]. This separation would help the precise analysis of both processes.In peripheral heavy-ion reactions due to the initial angular momentum, the initial state of the fluid dynamical stage of the collision dynamics has shear flow characteristics, and this leads to rotation [7] and even the Kelvin-Helmholtz instability (KHI) [8] in the reaction plane for a low-viscosity quark-gluon plasma. This possibility was indicated by high-resolution computational fluid dynamics (CFD) calculations using the Particle in Cell (PIC) method. We study the development of these processes in a (3 + 1)-dimensional (3 + 1)D configuration to describe the energy and momentum balance realistically. The presently used relativistic PICR hydro was the first, which included the QGP equation of state (EoS) [9], the y and p t spectra were evaluated and the softening of the EoS was predicted in 1994, leading to a strong change of p x (y)/a [or v 1 (y)], [10][11][12], which led to the prediction of the third flow component or antiflow [13]. This was then measured at the BNL Relativistic Heavy-Ion Collider (RHIC) and presented in 2006 [14]. Just as in the publications discussing the RHIC (including the Beam Energy Scan) results [15][16][17][18], here we also used the initial-state model assuming transparency and strong attractive fields with accurate impact-parameter dependence and rapidity distribution in the transverse plane [19]. This initial-state model is used as for all configurations assuming transparency and QGP. It assumes an initial interpenetration of Lorentz-contracted slabs (in most present models considered as Color Glass Condensate), and strong attractive coherent Yang-Mills fields act between these end slabs, with large string tension (according to the color rope model [20]). During the slowing down of these expanding fields the original net baryon charge is considered to be longitudinally uniformly distributed in the streak-by-streak expanding system and then, in the subsequent initial Riemann scaling expansion, the net baryon charge follows thi...