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Astron. Astrophys. 356, 287-300 (2000)

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The shock waves in decaying supersonic turbulence

M.D. Smith 1, M.-M. Mac Low 2,3 and J.M. Zuev 4

1 Armagh Observatory, College Hill, Armagh BT61 9DG, Northern Ireland
2 Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
3 Department of Astrophysics, American Museum of Natural History, 79th St. at Central Park West, New York, New York, 10024-5192, USA
4 JILA, University of Colorado, Boulder, Campus Box 440, Boulder, CO 80309, USA (mds@star.arm.ac.uk; mordecai@amnh.org; julia.zuev@colorado.edu)

Received 20 October 1999 / Accepted 25 January 2000

Abstract

We here analyse numerical simulations of supersonic, hypersonic and magnetohydrodynamic turbulence that is free to decay. Our goals are to understand the dynamics of the decay and the characteristic properties of the shock waves produced. This will be useful for interpretation of observations of both motions in molecular clouds and sources of non-thermal radiation.

We find that decaying hypersonic turbulence possesses an exponential tail of fast shocks and an exponential decay in time, i.e. the number of shocks is proportional to [FORMULA] for shock velocity jump v and mean initial wavenumber 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 Mach number shocks. The power loss peaks near a low-speed turn-over in an exponential distribution. An analytical extension of the mapping closure technique is able to predict the basic decay features. Our analytic description of the distribution of shock strengths should prove useful for direct modeling of observable emission. We note that an exponential distribution of shocks such as we find will, in general, generate very low excitation shock signatures.

Key words: hydrodynamics – shock waves – turbulence – ISM: clouds – ISM: kinematics and dynamics

Send offprint requests to: M.D. Smith

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© European Southern Observatory (ESO) 2000

Online publication: March 28, 2000
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