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We use a suite of cosmological hydrodynamic simulations, run by two fixedgrid codes, to investigate the properties of solenoidal and dilatationalmotions of the intergalactic medium (IGM), and the impact of numericalviscosity on turbulence in a LCDM universe. The codes differ only in thespatial difference discretization. We find that (1) The vortical motion growsrapidly 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, indicatingcomparable vortical and compressive motions at present. (2) Power spectra ofthe solenoidal velocity possess two regimes, $\propto k^{-0.89}$ and $\proptok^{-2.02}$, while the total and dilatational velocity follow the scaling$k^{-1.88}$ and $k^{-2.20}$ respectively in the turbulent range. The IGMturbulence may contain two distinct phases, the supersonic and post-supersonicphases. (3) The non-thermal pressure support, measured by the vortical kineticenergy, 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 thecosmic mean shows a preliminary positive correlation with the turbulencepressure support. (4) A relatively higher numerical viscosity would dissipateboth the compressive and vortical motions of the IGM into thermal energy moreeffectively, resulting in less developed vorticity, remarkably shortenedinertial range, and leading to non-negligible uncertainty in the thermalhistory of gas accretion. Shocks in regions outside of clusters aresignificantly suppressed by numerical viscosity since $z=2$, which may directlycause the different levels of turbulence between two codes.

Turbulence in the Inter-galactic Medium: Solenoidal and Dilatational Motions, and the Impact of Numerical Viscosity