The kinematics of air motions in and around the polar vortices in the Geophysical Fluid Dynamics Laboratory SKYHI general circulation model are investigated by means of a Lagrangian particle analysis. Particles initialized in the mesosphere and upper stratosphere rapidly descend to the middle stratosphere. This descent is unmixed in the sense that the isentropic mass transport into the vortex is less than 5% of the vortex mass per month. Transport out of the vortex is less than 10% of the vortex mass per month. The reversible component of the Lagrangian mean downward velocity (in isentropic coordinates) is approximated to better than 20% by the diabatic heating rate at the time mean location of the center of mass. The interplay between diabatic descent and horizontal mixing in causing the steepness of tracer contours (e.g., N2O) around the vortex edge is vividly illustrated in our trajectory experiments. These experiments also illustrate the limitations of the concept of “air parcel” within the midlatitude surf zone. The dynamics of polar descent are investigated by diagnosing the forcing of the residual circulation. In the upper stratosphere, diabatic descent inside polar vortices is driven by Eliassen‐Palm flux divergences associated with motions of period shorter than 2 days (presumably gravity waves) in the Antarctic, but of period greater than 3 days (presumably planetary waves) in the Arctic. In the lower stratosphere, long period processes, mainly from the 10 to 1 hPa region, produce descent near the vortex edge in both hemispheres.