Vortical processes in astrophysical disks (PhD Thesis, Columbia University, May 1995)

Disks that are not too thick are analyzed with {\it shallow gas} theory. Nonlinear conditions for stability of steady disks are derived and found to be functions of the steady distributions and wave properties of {\em surface density} and {\em potential vorticity}. Finite amplitude asymmetry produced strong nonlinear instability mechanisms in the numerical experiments. Waves of vorticity drove axisymmetrization but are coordinated with waves of density and potential vorticity whose effect was efficient mixing of mass and angular momentum. All mixing mechanisms - even axisymmetric - produced a potential vorticity function that decreases monotonically with the radius, as is consistent with the stability condition. Transition to identifiable turbulence did not occur in the models, but small scale forcing experiments confirmed the presence of an inverse energy cascade characteristic of geostrophic turbulence. The cascade is a measure of mixing but its effective regime was spatially restricted to a sub-disk scale $L \sim 0.1 r_{disk}$ by the effects of compressibility and shear. Coherent long-lived vortices only reach this size. Vortices produced by instability and vortices directly superposed on the disk are also spatially limited in this way. Waves and vortices were efficient mixing agents in the model disk producing an effective $\alpha \sim O(10^{-1})$ and therefore provided an unexpected mechanism of angular momentum transport and mass accretion. The cascade of enstrophy to smaller scales - where it could be efficiently dissipated by viscosity - also accounted for angular momentum transport as it accompanies the enstrophy removal.

Significant radiation permeates disks so we solve the linearized stability problem obtained from a formal asymptotic reduction of a fully coupled radiation and fluid. The case of thermal radiation with flux through plane couette flow has weak unstable modes that are variations of ordinary compressible shear modes. When the flux is strong, the unstable modes are dominantly radiative and the instability appears as a flicker.