Vortical Motions of Baryonic Gas in the Cosmic Web: Growth History and Scaling Relation

The vortical motions of the baryonic gas residing in large scale structures are investigated by cosmological hydrodynamic simulations. Proceeding in the formation of the cosmic web, the vortical motions of baryonic matter are pumped up by baroclinity in two stages, i.e., the formation of sheets, and filaments. The mean curl velocity are about $< 1$, 1-10, 10-150, 5-50 km/s in voids, sheets, filaments and knots at $z=0$, respectively. The scaling of the vortical velocity of gas can be well described by the She-Leveque hierarchical turbulence model in the range of $l<0.65(1.50) h^{-1}$ Mpc in simulation of box size 25(100) $h^{-1}$ Mpc. The fractal Hausdorff dimension of vortical motions, $d$, revealed by velocity structure functions, is $\sim 2.1-2.3$($\sim 1.8-2.1$). It is slightly larger than the fractal dimension of mass distribution in filaments, $\textit{D}^f \sim 1.9-2.2$, and smaller than the fractal dimension of sheets, $\textit{D}^s \sim 2.4-2.7$. The vortical kinetic energy of baryonic gas is mainly transported by filaments. Both the scaling of mass distribution and vortical velocity increments show distinctive transition at the turning scale of $\sim 0.65(1.50) h^{-1}$ Mpc, which may be closely related to the characteristic radius of density filaments.