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

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