Shock Waves and Energy Dissipation in Magnetohydrodynamic Turbulence

Shock waves play an important role in turbulent astrophysical media by compressing the gas and dissipating the turbulent energy into the thermal energy. We here study shocks in magnetohydrodynamic turbulence using high-resolution simulations. Turbulent Mach numbers of $\mathcal{M}_\text{turb}=0.5-7$ and initial magnetic fields of plasma beta $\beta_0=0.1 - 10$ are considered, targeting turbulences in interstellar and intracluster media. Specifically, we present the statistics of fast and slow shocks, such as the distribution of shock Mach numbers ($M_\text{s}$) and the energy dissipation at shocks, based on refined methodologies for their quantifications. While most shocks form with low $M_\text{s}$, strong shocks follow exponentially decreasing distributions of $M_\text{s}$. More shocks appear for larger $\mathcal{M}_\text{turb}$ and larger $\beta_0$. Fast shock populations dominate over slow shocks if $\beta_0\gg1$, but substantial populations of slow shocks develop in the cases of $\beta\lesssim1$, i.e., strong background fields. The shock dissipation of turbulent energy occurs preferentially at fast shocks with $M_\text{s}\lesssim$ a few to several, and the dissipation at strong shocks shows exponentially decreasing functions of $M_\text{s}$. The energy dissipation at shocks, normalized to the energy injection, $\epsilon_\text{shock}/\epsilon_\text{inj}$, is estimated to be in the range of $\sim0.1-0.5$, except for the case of $\mathcal{M}_\text{turb}=0.5$ and $\beta_0=0.1$ where the shock dissipation is negligible. The fraction decreases with $\mathcal{M}_\text{turb}$; it is close to $\sim0.4-0.6$ for $\mathcal{M}_\text{turb}=0.5$, while it is $\sim0.1-0.25$ for $\mathcal{M}_\text{turb}=7$. The rest of the turbulent energy is expected to dissipate through the turbulent cascade.