Excitation of transient Rossby waves on the stratospheric polar vortex and the barotropic sudden warming

The excitation of Rossby waves on the edge of the stratospheric polar vortex, due to time-dependent topographic forcing, is studied analytically and numerically in a simple quasiggeostrophic f-plane model. When the atmosphere is compressible, the linear response of the vortex 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. The relative magnitude of the two responses, in terms of total angular pseudomomentum, depends on the ratio of the horizontal scale of the forcing to the Rossby radius. Under typical stratospheric conditions the barotropic response is found to dominate. Nonlinear simulations confirm that the linear results remain relevant to understanding the response in cases when strongly nonlinear Rossby wave breaking ensues. It is shown that a sudden warming, or rapid increase in vortex angular pseudomomentum, can be generated at much lower forcing amplitudes when the barotropic mode is resonantly excited compared to when the upward-propagating waves are excited. A numerical simulation of a "barotropic sudden warming" due to excitation of the barotropic mode by a relatively weak topographic forcing is described.