| This dissertation discusses two different problems in astrophysical turbulence.; The first problem is the nature of the turbulence in the interstellar medium, specifically in cool molecular clouds and star-forming regions. Local overdensities (clouds) in these regions are known to be supersonically turbulent, with typical Mach numbers on the order of ten or more. We develop a model for turbulence in these clouds in which individual clouds dissipate their turbulent kinetic energy internally, and this internal dissipation is balanced in the mean by the injection of kinetic energy from strong shocks that arrive intermittently. Physically, these shocks correspond to the shocks from supernovae as well as other explosive events. We find that such a model nicely predicts the existence of large internal velocities with non-Gaussian statistics, as well as the observed phenomenological relationship between cloud size and line width. We also discuss star formation within the context of this model.; The second problem is a treatment of certain aspects of the hydrodynamics of astrophysical accretion disks. We specifically consider non-self-gravitating disks in the thin disk limit. These systems are, in a hydrodynamic sense, stable according to the Rayleigh criterion, and yet there is mounting evidence that the dissipative and transport processes that must be at work within these disks are hydrodynamic in nature at least some of the time. We apply the developing theory of transition to turbulence via large linear transient amplification of initial disturbances, which depends upon the non-self-adjoint nature of the differential operator that describes the dynamics of perturbations to the background state in these systems. We find that small initial perturbations can be tailored to produce large growth in accretion disks, despite the absence of any linear instability. Furthermore, perturbations to the operator that governs the growth of perturbations to the flow can create an operator that possesses modes with unbounded growth. The size of the perturbation to the operator that is necessary to make the governing equations have unstable solutions is asymptotically small as a function of Reynolds number. |
