A modified version of the Charney-Drazin criterion shows that a stratospheric polar vortex of given strength will support the upward propagation of vortex Rossby waves whose frequencies lie within a certain range. A complete description of vortex perturbations, however, requires the consideration of an additional mode with a barotropic structure, in which the vortex deforms uniformly in height. The first part of the talk will describe the theory of the upward propagating and barotropic modes and, by comparing simple models and observations, will demonstrate the importance of the barotropic mode in the dynamics of the stratospheric sudden warming. The second part of the talk will discuss a dynamical constraint on the structure of stratospheric wave breaking based on a consideration of the mixing of potential vorticity. The constraint provides an explicit relation between the strength of the stratospheric wave driven residual circulation (or component of the Brewer