The distribution of shock waves in driven supersonic turbulence

Supersonic turbulence generates distributions of shock waves. Here, we anal yse the shock waves in three-dimensional numerical simulations of uniformly driven supersonic turbulence, with and without magnetohydrodynamics and se lf-gravity. We can identify the nature of the turbulence by measuring the d istribution of the shock strengths. We find that uniformly driven turbulence possesses a power law distribution of fast shocks with the number of shocks inversely proportional to the squ are root of the shock jump speed. A tail of high speed shocks steeper than Gaussian results from the random superposition of driving waves which decay rapidly. The energy is dissipated by a small range of fast shocks. These r esults contrast with the exponential distribution and slow shock dissipatio n associated with decaying turbulence. A strong magnetic field enhances the shock number transverse to the field d irection at the expense of parallel shocks. A simulation with self-gravity demonstrates the development of a number of highly dissipative accretion sh ocks. Finally, we examine the dynamics to demonstrate how the power-law beh aviour arises.