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Center for Nonlinear Studies |
My research examines turbulence in fluids dominated by rotation and stratification such as the atmosphere, oceans, and gaseous disks surrounding young stars. Asymptotic expansions in the conservation of energy, mass, and momentum equations lead to reduced equation sets which are modeled numerically using pseudo-spectral methods. Two numerical models were developed for this work: a quasi-geostrophic (QG) model to investigate large-scale motion of the atmosphere and oceans, and a protoplanetary disk model which simulates vortex formation and evolution in gaseous stellar disks. The QG model is used to characterize slanted QG, an asymptotic regime where the full planetary rotation vector is kept, instead of just the vertical component as in standard QG. This regime is appropriate for meso-scale dynamics, where horizontal and vertical scales are comparable, as well as near the equator where the vertical component of the planetary rotation goes to zero. 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. The structure of three-dimensional quasi-geostrophic (3D QG) turbulence is quantitatively different from two-dimensional (2D) barotropic turbulence. In both regimes the vortex cores, which induce non-Gaussian velocity profiles, are surrounded by vorticity filaments, which induce Gaussian velocity profiles. The majority of the kinetic energy in 2D turbulence is due to the cores, resulting in a non-Gaussian total velocity field. In contrast, more kinetic energy in 3D QG turbulence is due to the filaments, resulting in a nearly Gaussian total velocity field. Thus filamentary structures play a much more dominant role in 3D QG dynamics than in 2D turbulence. The protoplanetary disk model is a reduced, coupled system for vorticity and temperature which includes background rotation, temperature and surface density profiles. Model simulations with initial temperature perturbations and zero initial vorticity produce coherent, long-lived vortices within several orbital periods through baroclinic vorticity production. This study identifies regions of parameter space where shear due to differential rotation inhibits vortex formation, as well as regions of parameter space where strong vortices form.