Ellipsoidal vortices beyond the quasi-geostrophic approximation

As a model of geophysical vortices, we study numerically the behavior of an ellipsoidal volume of uniform potential vorticity in a non-hydrostatic, rotating stratified flow. Previous studies on ellipsoidal vortices mainly focus on the quasi-geostrophic regime. Here, we aim to determine the effects of ageostrophy on the stability, evolution and the final fate of the vortices. Cyclonic and anti-cyclonic vortices of various aspect ratios are investigated. Generally, cyclonic vortices with roughly circular cross section tend to be more stable. In the cases when the vortices become unstable, a wide range of nonlinear evolution is observed including tumbling, shape vacillation, splitting and filaments shedding. Diagnostics concerning the vortex rotation rate and the degree of ``imbalance,'' which quantifies the amount of internal gravity waves emission, will be presented.