Rotation in an exact hydrodynamical model

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.

Figure 1

The time dependence of the kinetic energy of the expansion, $E_K$, of the internal energy, $E_{\mathrm{int}}$, and the rotational energy, $E_{\mathrm{rot}}$, per nucleon in the exact model with the initial conditions described above. The kinetic energy of the expansion is increasing, at the cost of the decreasing internal energy and the slower decreasing rotational energy. The rotational energy is decreasing to half of the initial one in 2.1 $\mathrm{fm}/c$.

Figure 2

The time dependence of the velocity of expansion in the transverse radial direction, $v_R$, and in the direction of the axis of the rotation, $v_Y$.

Figure 3

The time dependence of the radial, $R$, and the $y$-axis-directed size, $Y$, of the expanding system. As the $y$ directed velocity is initially larger and its change is relatively smaller the change of the rate of increase is hardly visible.