Effects of Forcing on Shocks and Energy Dissipation in Interstellar and Intracluster Turbulences

Abstract

Observations indicate that turbulence in the interstellar medium (ISM) is supersonic (M turb ≫ 1) and strongly magnetized (β ∼ 0.01–1), while in the intracluster medium (ICM) it is subsonic (M turb ≲ 1) and weakly magnetized (β ∼ 100). Here, M turb is the turbulent Mach number and β 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 weighted essentially nonoscillatory 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 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 turb ≈ 10 and β ∼ 0.1, the fraction of the turbulent energy dissipated at shocks is estimated to be ∼15%, not sensitive to the forcing mode. In contrast, in 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 the ensuing shock dissipation is in the range of ∼10%–35% in the ICM models with M turb ≈ 0.5 and β ∼ 106. The rest of the turbulent energy should be dissipated through turbulent cascade.