The excitation of the barotropic mode of a columnar vortex and wave-2 sudden warmings

The excitation of the barotropic mode of a columnar vortex and wave-2 sudden warmings

The excitation of Rossby waves on the edge of the stratospheric polar vortex is studied analytically and numerically in a simple quasi-geostrophic $f$-plane model. The Rossby waves are excited by a time-dependent wave-2 topographic forcing which represents the influence of a dynamically active troposphere. The linear response of the vortex to the forcing is found to have two distinct components. The first is a spectrum of upward propagating waves that are excited by forcing with temporal frequencies within a fixed `Charney-Drazin' range that depends on the angular velocity at the vortex edge and the vortex Burger number. The second component of the response is a barotropic mode, which is excited by forcing with a fixed temporal frequency outside the Charney-Drazin range. Nonlinear simulations reveal that excitation of the upward propagating waves leads to wave amplification and breaking at high altitudes. Excitation of the barotropic mode, by contrast, leads to the vortex becoming more uniformly more elliptical and, at moderate to large forcing amplitudes, can cause the vortex to divide in two. Results from numerical simulations of these `barotropic sudden warmings' are presented, and the relationship between the vertical structure of the vortex and the topology of the warming itself is discussed with reference to observations.