Turbulence is ubiquitous in the universe and plays an important role in diverse astrophysical processes, from star formation to galaxy evolution. Measuring turbulence in astrophysics, however, is not always easy. In this talk, I will discuss novel techniques my group recently developed in the analysis of turbulence in the interstellar medium (ISM) and the intracluster medium (ICM). We study the motions of young stars in the Orion Molecular Cloud Complex, using the full 6-dimensional measurements of positions and velocities provided by the APOGEE-2 and Gaia DR2 surveys. We compute the velocity structure functions (VSFs) of the stars in six different groups within the Orion Complex, and find that the motions of stars in all diffuse groups exhibit strong characteristics of turbulence. Our VSFs also show features supporting local energy injection from supernovae. We have also analyzed the motions of multiphase gas in the ICM of three nearby galaxy clusters: Perseus, Abell 2597 and Virgo. We show that the motions of the filamentary cool clouds are turbulent, and the turbulence is driven by feedback from the SMBHs in the centers of these clusters. The smallest scales we probed are comparable to the mean free path in the hot ICM. The detection of turbulence on these scales provides strong evidence that isotropic viscosity is suppressed in the hot plasma.
