The shock waves in decaying supersonic turbulence

We here analyse numerical simulations of supersonic, hypersonic and magneto hydrodynamic turbulence that is free to decay. Our goals are to understand the dynamics of the decay and the characteristic properties of the shock wa ves produced. This will be useful for interpretation of observations of bot h motions in molecular clouds and sources of non-thermal radiation. We find that decaying hypersonic turbulence possesses an exponential tail o f fast shocks and an exponential decay in time, i.e. the number of shocks i s proportional to t exp(-ktv) for shock velocity jump v and mean initial wa venumber k. In contrast to the velocity gradients, the velocity Probability Distribution Function remains Gaussian with a more complex decay law. The energy is dissipated not by fast shocks but by a large number of low Ma ch number shocks. The power loss peaks near a low-speed turn-over in an exp onential distribution. An analytical extension of the mapping closure techn ique is able to predict the basic decay features. Our analytic description of the distribution of shock strengths should prove useful for direct model ing of observable emission. We note that an exponential distribution of sho cks such as we find will, in general, generate very low excitation shock si gnatures.