Turbulence in the Inter-galactic Medium: Solenoidal and Dilatational
  Motions, and the Impact of Numerical Viscosity
  We use a suite of cosmological hydrodynamic simulations, run by two fixed
grid codes, to investigate the properties of solenoidal and dilatational
motions of the intergalactic medium (IGM), and the impact of numerical
viscosity on turbulence in a LCDM universe. The codes differ only in the
spatial difference discretization. We find that (1) The vortical motion grows
rapidly since $z=2$, and reaches $\sim 10 km/s -90 km/s$ at $z=0$. Meanwhile,
the small-scale compressive ratio $r_{CS}$ drops from 0.84 to 0.47, indicating
comparable vortical and compressive motions at present. (2) Power spectra of
the solenoidal velocity possess two regimes, $\propto k^{-0.89}$ and $\propto
k^{-2.02}$, while the total and dilatational velocity follow the scaling
$k^{-1.88}$ and $k^{-2.20}$ respectively in the turbulent range. The IGM
turbulence may contain two distinct phases, the supersonic and post-supersonic
phases. (3) The non-thermal pressure support, measured by the vortical kinetic
energy, is comparable with the thermal pressure for $\rho_b \simeq 10-100$, or
$T <10^{5.5} K$ at $z=0.0$. The deviation of the baryon fraction from the
cosmic mean shows a preliminary positive correlation with the turbulence
pressure support. (4) A relatively higher numerical viscosity would dissipate
both the compressive and vortical motions of the IGM into thermal energy more
effectively, resulting in less developed vorticity, remarkably shortened
inertial range, and leading to non-negligible uncertainty in the thermal
history of gas accretion. Shocks in regions outside of clusters are
significantly suppressed by numerical viscosity since $z=2$, which may directly
cause the different levels of turbulence between two codes.
