Two models are introduced in this paper: A slanted quasi-geostrophic (QG) model used to study geophysical turbulence and a protoplanetary disk model of the gas that surrounds young stars. The slanted QG model is a low order derivation of the primitive equations that differs from standard QG in that the aspect ratio is order one. The equations of motion in this asymptotic regime keep the full rotation vector instead of just the vertical component as in standard QG, indicating that the slanted limit may be a good model to study dynamics of stratified flows near the equator. Numerical experiments from a three dimensional, periodic, pseudo-spectral model of slanted QG show that vortices align with the axis of rotation, a result which is predicted analytically for the nonviscous equation.

Protoplanetary disk models are used to study Rossby waves, shear instabilities, and vortex formation in gas disks around young stars that eventually lead to planetary formation. A reduced,coupled system for vorticity and temperature is derived from the anelastic equations and shown to yield Rossby waves. A two dimensional pseudospectral model of this system will be used to investigate the dynamical behavior of the disk.

Committee members: Harvey Segur, Keith Julien, Jeff Weiss (PAOS), Glen Stewart (LASP), Bengt Fornberg