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Supersonic flows in the interstellar medium (ISM) are believed to be a keydriver of the molecular cloud formation and evolution. Among molecular clouds'properties, the ratio between the solenoidal and compressive modes ofturbulence plays important roles in determining the star formation efficiency.We use numerical simulations of supersonic converging flows of the warm neutralmedium (WNM) resolving the thermal instability to calculate the early phase ofmolecular cloud formation, and investigate the turbulence structure and thedensity probability distribution function (density PDF) of the multiphase ISM.We find that both the solenoidal and compressive modes have their powerspectrum similar to the Kolmogorov spectrum. The solenoidal (compressive) modesaccount for >~80% (<~20%) of the total turbulence power. When we consider boththe cold neutral medium (CNM) and the thermally unstable neutral medium (UNM)up to T <~ 400 K, the density PDF follows the log-normal distribution whosewidth sigma_s is well explained by the known relation from the isothermalturbulence as sigma_s = ln(1 + b^2 * M^2) (where b is the parameterrepresenting the turbulence mode ratio and M is the turbulent Mach number). Thedensity PDF of the CNM component alone (T <= 50 K), however, exhibits anarrower sigma_s by a factor of ~ 2. These results suggest that observationalestimations of b based on the CNM density PDF requires the internal turbulencewithin each CNM clump but not the inter-clump relative velocity, the latter ofwhich is instead powered by the WNM/UNM turbulence.

Nature of supersonic turbulence and density distribution function in the multiphase interstellar medium