  Supernova explosions, active galactic nuclei jets, galaxy--galaxy
interactions and cluster mergers can drive turbulence in the circumgalactic
medium (CGM) and in the intracluster medium (ICM). However, the exact nature of
turbulence forced by these sources and its impact on the different statistical
properties of the CGM/ICM and their global thermodynamics is still unclear. To
investigate the effects of different types of forcing, we conduct high
resolution ($1008^3$ resolution elements) idealised hydrodynamic simulations
with purely solenoidal (divergence-free) forcing, purely compressive
(curl-free) forcing, and natural mixture forcing (equal fractions of the two
components). The simulations also include radiative cooling. We study the
impact of the three different forcing modes (sol, comp, mix) on the morphology
of the gas, its temperature and density distributions, sources and sinks of
enstrophy, i.e., solenoidal motions, as well as the kinematics of hot
($\sim10^7~\mathrm{K}$) X-ray emitting and cold ($\sim10^4~\mathrm{K}$)
H$\alpha$ emitting gas. We find that compressive forcing leads to stronger
variations in density and temperature of the gas as compared to solenoidal
forcing. The cold phase gas forms large-scale filamentary structures for
compressive forcing and misty, small-scale clouds for solenoidal forcing. The
cold phase gas has stronger large-scale velocities for compressive forcing. The
natural mixture forcing shows kinematics and gas distributions intermediate
between the two extremes, the cold-phase gas occurs as both large-scale
filaments and small-scale misty clouds.
