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Turbulence is essential for understanding the structure and dynamics ofmolecular clouds and star-forming regions. There is a need for adequate toolsto describe and characterize the properties of turbulent flows. One-pointprobability distribution functions (pdf's) of dynamical variables have beensuggested as appropriate statistical measures and applied to several observedmolecular clouds. However, the interpretation of these data requires comparisonwith numerical simulations. To address this issue, SPH simulations of drivenand decaying, supersonic, turbulent flows with and without self-gravity arepresented. In addition, random Gaussian velocity fields are analyzed toestimate the influence of variance effects. To characterize the flowproperties, the pdf's of the density, of the line-of-sight velocity centroids,and of the line centroid increments are studied. This is supplemented by adiscussion of the dispersion and the kurtosis of the increment pdf's, as wellas the spatial distribution of velocity increments for small spatial lags. Fromthe comparison between different models of interstellar turbulence, it followsthat the inclusion of self-gravity leads to better agreement with the observedpdf's in molecular clouds. The increment pdf's for small spatial lags becomeexponential for all considered velocities. However, all the processesconsidered here lead to non-Gaussian signatures, differences are only gradual,and the analyzed pdf's are in addition projection dependent. It appearstherefore very difficult to distinguish between different physical processes onthe basis of pdf's only, which limits their applicability for adequatelycharacterizing interstellar turbulence.

One‐Point Probability Distribution Functions of Supersonic Turbulent Flows in Self‐gravitating Media