Effects of Forcing on Shocks and Energy Dissipation in Interstellar and
  Intracluster Turbulences
  Observations indicate that turbulence in the interstellar medium (ISM) is
supersonic ($M_{\rm turb}\gg1$) and strongly magnetized ($\beta\sim0.01-1$),
while in the intracluster medium (ICM) it is subsonic ($M_{\rm turb}\lesssim1$)
and weakly magnetized ($\beta\sim100$). Here, $M_{\rm turb}$ is the turbulent
Mach number and $\beta$ is the plasma beta. We study the properties of shocks
induced in these disparate environments, including the distribution of the
shock Mach number, $M_s$, and the dissipation of the turbulent energy at
shocks, through numerical simulations using a high-order accurate code based on
the WENO scheme. In particular, we investigate the effects of different modes
of the forcing that drives turbulence: solenoidal, compressive, and a mixture
of the two. In the ISM turbulence, while the density distribution looks
different with different forcings, the velocity power spectrum, $P_v$, on small
scales exhibits only weak dependence. Hence, the statistics of shocks depend
weakly on forcing either. In the ISM models with $M_{\rm turb}\approx10$ and
$\beta\sim0.1$, the fraction of the turbulent energy dissipated at shocks is
estimated to be $\sim15~\%$, not sensitive to the forcing mode. In contrast, in
the ICM turbulence, $P_v$ as well as the density distribution show strong
dependence on forcing. The frequency and average Mach number of shocks are
greater for compressive forcing than for solenoidal forcing, so is the energy
dissipation. The fraction of ensuing shock dissipation is in the range of
$\sim10-35~\%$ in the ICM models with $M_{\rm turb}\approx0.5$ and
$\beta\sim10^6$. The rest of the turbulent energy should be dissipated through
turbulent cascade.
