Figure 1

Growth of the initial stage of Kelvin-Helmholtz instability in a $1.38A+1.38A$ TeV peripheral, $b=0.7b_{\max }$, $\mathrm{Pb}+\mathrm{Pb}$ collision in a relativistic CFD simulation using the PIC method. We see the positions of the marker particles (Lagrangian markers with fixed baryon number content) in the reaction plane. The calculation cells are $dx=dy=dz=0.4375$ fm and the time step is 0.04233 fm/$c$ The number of randomly placed marker particles in each fluid cell is $8^3$. The axis labels indicate the cell numbers in the $x$ and $z$ (beam) direction. The initial development of a KH-type instability is visible from $t=1.5$ up to $t=7.41$ fm/$c$, corresponding to 35 to 175 calculation time steps.Reuse & Permissions

Figure 2

Time evolution of the flow in a $1.38A+1.38A$ TeV peripheral, $b=0.5b_{\max }$ $\mathrm{Pb}+\mathrm{Pb}$ collision. The calculation cells are $dx=dy=dz=0.585$ fm and the time step is 0.08466 fm/$c$. The number of randomly placed marker particles in each fluid cell is $8^3$. In contrast to Fig. 1 the KH instability does not develop during the initial $\sim 8$ fm/$c$ time, due to the increased numerical viscosity and the similar length and height of the initial state. Thus the sides of the fluid provide a stiffer formation and the system rather rotates as a solid body, instead of forming an expanding turbulent, rotating shell. Due to angular momentum conservation the rotation slows down as the system expands.Reuse & Permissions

Figure 3

Comparison of the flow pattern in the reaction plane in $1.38A+1.38A$ TeV peripheral, $\mathrm{Pb}+\mathrm{Pb}$ collisions at two impact parameters: $b=0.5b_{\max }$ (left column) and $b=0.7b_{\max }$ (right column), at a late stage of 10.16 fm/$c$ (240 time steps). By this time an instability wave is also noticeable at $b=0.5b_{\max }$. The resolution increases from the top to the bottom as $dx=0.585,0.4375,0.35$ fm (i.e., $N_R=R_{\mathrm{Pb}}/dx=12,16,20$). The numbers of marker particles were $8^3$, $6^3$, and $5^3$ for these resolutions, so that each of the marker particles carried about the same amount of baryon charge: $5.61\times {10}^{-5}$, $5.61\times {10}^{-5}$, and $4.97\times {10}^{-5}$. For the impact parameter $b=0.5b_{\max }$, independently of the resolution and numerical viscosity, the rotation of the dividing plane is 2 degrees, and the amplitude of the KH instability wave is not bigger than 0.35 fm. For the impact parameter $b=0.7b_{\max }$ the rotation of the dividing plane is $3.75$ degrees for all resolutions, but the amplitude of the KH instability wave is increasing with increasing resolution (decreasing numerical viscosity) as 0.7, 0.9, and 1.1 fm.Reuse & Permissions

Figure 4

The velocity profile in the beam direction as a function of the $x$ coordinate, at different times, 4, 40, 80, 120, 160, 200, and 240 time steps of 0.04233 fm/$c$ for $b=0.7b_{\max }$, cell size $dx=0.35$ fm, and $7^3$ marker particles per fluid cell. The velocity is plotted in the reaction plane (at $y=0$ and $z=0$), and it is antisymmetric in the $\pm x$ direction, but only the upper $x>0$ half of the reaction plane is plotted. In the CFD calculation the mirror symmetry is exact.Reuse & Permissions

Figure 5

The detailed view of the marker particle positions in the lower half of the initial-state markers after 175 time steps. A $1.38A+1.38A$ TeV energy $\mathrm{Pb}+\mathrm{Pb}$ peripheral collision is shown, at impact parameter $b=0.7b_{\max }$ with $7^3=343$ markers per initial, normal-density-fluid cell resolution. The lines across the collision center point indicate the initial dividing axis, the change of this axis due to rotation, and the additional change of rotation arising from the start-up of a Kelvin-Helmholtz type of instability. This additional effect more than doubles the rotation. In this calculation the cell size is $dx=dy=dz=0.35$ fm, with a total number of $1814814$ marker particles.Reuse & Permissions