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Astron. Astrophys. 362, 333-341 (2000)

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7. Conclusions

We have analysed numerical simulations of uniformly driven supersonic, magnetohydrodynamic and self-gravitating turbulence. Below a critical jump speed, we find a power law distribution of fast shocks with the number of shocks inversely proportional to the square root of the shock jump speed. Hence, unlike the decaying case, the driven case possesses an `inertial range' of shock strengths. This range is, however, dynamically passive, being mediated by strong shocks injected at a higher knee in the distribution. The knee is mainly responsible for the dissipation of energy, and thus the power-law range may only have a weak observational signature. This will be explored in the following paper of this series.

These results contrast with the exponential distribution and slow shock dissipation associated with decaying turbulence described in Paper 1.

A strong magnetic field does not alter the shape of the shock number distributions. It enhances the shock number transverse to the field direction at the expense of parallel shocks. The distribution of parallel shocks is, however, extended to higher jump speeds. Transverse waves thus appear to find support in the magnetic pressure.

A simulation with self-gravity demonstrates the development of a number of highly dissipative accretion shocks. These shocks are rare and are not apparent in the number distributions. The shock number distribution demonstrates a gradual curvature rather than a power-law. This implies that high-speed shocks can be maintained by gravitational acceleration.

Finally, we have shown how the power-law behaviour may arise. No substantial theory has been developed to predict this inverse square root law. The power law is closely related to the distribution in absolute shock speeds, which is shown to be flat. The particular power law is predicted to depend on the type of driver.

The energy is dissipated in shocks mainly associated with the denser regions of the clouds formed by the large scale wave motions. Numerous other shocked regions are scattered throughout. Very strong shocks are associated with the collapsing cores in the self-gravitating case.

Our results must be considered within the context of the imposed models. While turbulence has been pinned down in many studies, further studies have simply extended the number of pins required. Extensions to this work include: (1) the shock distributions corresponding to non-uniform drivers, (2) the spatial propagation of turbulent energy and (3) the observable signatures: the spectral energy distributions derived from the shock distributions,

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© European Southern Observatory (ESO) 2000

Online publication: October 30, 19100