A note on compressibility and energy cascade in turbulent molecular clouds

Observed velocity-size correlations are reexamined in the light of an improved theory of turbulent energy cascade that is developed. It is shown that observed velocity-size correlations cannot be compared with the Kolmogorov law, which is based on incompressible turbulent flow. The fact that the log v-log(l/rho) scaling law (v the turbulent velocity, l the associated region size, and rho the fluid density) predicted for compressible energy cascade is always steeper than that observed in molecular clouds indicates the injection rather than the dissipation of mechanical energy at smaller scales of motion. It is also shown that the concept of strict energy cascade may not be generally applicable in the interstellar medium. The agreement between theory and observation turns out to be best for small cool clouds and cloud cores, suggesting that, for these regions at least, the dominant process in establishing the observed v-l-rho correlation is a turbulent energy cascade.