Nonlinear oscillatory evolution of a baroclinically unstable geostrophic vortex

In a two-layer quasi-geostrophic model, we numerically investigate the nonlinear evolution of a baroclinically unstable geostrophic vortex. For perturbations with a moderate growth rate and a weak amplitude and weak viscosity, a regime of regular oscillation is attained. This regime has a quasi-periodic reversal of the vertical phase shift between the flow patterns in each layer, with a corresponding back-and-forth potential energy transfer between the mean vortex state and the fluctuation pattern. This oscillating vortex, averaged in a frame of reference co-rotating with the angular velocity of each layer, has an elliptical horizontal configuration with a simple relation between potential vorticity and co-rotating streamfunction. Simulations with smaller Burger or Reynolds number or larger initial perturbation amplitude show less regularity in the oscillation and eventually result in vortex breaking.