The quasi-geostrophic (QG) potential vorticity equation is a reduced model for stratified, rotating flows which is employed in atmospheric and ocean dynamics. I am working on an alternate asymptotic derivation dubbed "Slanted QG" where the full rotation vector is kept, which may have applications for low latitude dynamics.
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. A two dimensional pseudospectral model of this system will be used to investigate the dynamical behavior of the disk.