Protoplanetary disks play a key role in star and planet formation processes. Turbulence in these disks, which arises from the magnetorotational instability (MRI), not only causes accretion of mass onto the central star, but also sets the conditions for processes such as dust settling, planetesimal formation, and planet migration. However, the exact nature of this turbulence is still not very well constrained in these systems.
In this talk, I will first present recent numerical simulations of magnetohydrodynamic (MHD) turbulence in protoplanetary disks that point to the importance of large scale, vertical magnetic fields in driving disk accretion through both turbulent processes and laminar magnetic stresses, such as those induced via magnetic winds. I will then describe new work, utilizing both state-of-the-art numerical simulations and powerful new radio observations, to directly link numerical predictions for the turbulent velocity structure of protoplanetary disks to observations by the Atacama Large Millimeter Array (ALMA). ALMA's unprecedented resolution and sensitivity will allow us to generate a three-dimensional map of disk turbulence by measuring the turbulent broadening component of molecular lines at different disk heights and radii. A direct comparison between the observed turbulence values and those obtained from simulations will strongly constrain our theoretical understanding of these disks. I will conclude with an outlook for protoplanetary disk studies, and in particular how our current results may influence studies of planet formation processes and the construction of exoplanetary systems.