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.
