CONCLUSIONS

In this work we have presented 3D simulations of compressible turbulence in an interstellar context. We have discussed the differences between the representations of the data in physical and position-velocity (PV) spaces. We then presented preliminary results of a Principal Component Analysis of the simulations, comparing with an analogous study of molecular-line data by Heyer (1998). Our main results are as follows:

• We have also performed isothermal simulations (not shown here) without star formation, the magnetic field nor heating and cooling. The structure in those simulations is much less resemblant of the observational CO data in PV space than the ISM simulation, suggesting such physical agents are significantly more important in determining the structure than the cooling functions.

• The PV representation of the spatial gas density distribution is strongly influenced by the spatial velocity distribution.

• Localization in physical space does not necessarily correspond to localization in PV space, and viceversa.

• The PCA results imply that smaller velocity differences occur at smaller spatial separations. This result is also verified in the observational data of HB99, supporting the claim that this is a manifestation of the clouds being in a turbulent regime.

• Power-law fits to the $\Delta v$-R relationship obtained from PCA results appear to agree with the empirical relation found by HB99, namely $\alpha = \beta/3$, where $\alpha$ is the exponent in the $\Delta v$-R relation and $\beta$ is the spectral index. However, the low resolution of the data causes large uncertainties, and higher spatial and velocity relsolutions are needed before a conclusive result can be obtained.

We gratefully acknowledge useful discussions with Mark Heyer. The numerical simulation was performed at the Cray C98 of IDRIS, France.