Vorticity and mixing in disks

Disks play a role in many astrophysical phenomena, typically as mixers of angular momentum. In most cases, we can think of the disk as an astro-fluid-dynamical phenomenon responsible for the redistribution of matter and angular momentum in the universe - concentrating the matter at its center and dispersing the angular momentum as far from the center as possible. How the disk is able to mix as efficiently as observations suggest is an unsolved problem, though it is unlikely that there is an all-encompassing explanation satisfactory for all disks. The redistribution of angular momentum this way in an orbital ``flow'' depends on there being anisotropic internal stresses (viscosity) within the disk$ ^1$. In a simple fluid, molecular viscosity, turbulent viscosity and wave interaction are important mechanisms for providing such stresses, although molecular viscosity is negligible for most length scales of the disk. When strong magnetic fields are present or the disk is very particulate (to cite two examples) mixing may be dominated by magnetic or collisional effects, respectively. However, even in the absence of these last two effects, the behavior of a general continuum (fluid) disk is not a completely solved problem. On the contrary, little is fully understood about the behavior of rapidly rotating strongly sheared fluid layers, even as they occur in the laboratory. This study addresses the disk in a simplified incarnation based on the premise that there are fundamental fluid dynamical questions to be answered before developing more complete models. While astronomical studies often stress the distinctions among different manifestations of disks and relevant boundary conditions (source of material infall, presence of a companion, etc.), we argue that some of the essential actions of disks are performed by dynamical processes that occur on the shortest of all disk timescales for which radial infall velocities ( $u_r$ ) and boundary conditions are largely negligible.