Wind fields from a numerical simulation are used to give a detailed Lagrangian picture of air flow in the middle atmosphere of the southern hemisphere in winter and early spring 1991. Trajectories for many thousands of air particles exhibit rapid descent of mesospheric air into the stratospheric polar vortex, revealing its organizing and structure-preserving properties. Results are used to account for measurements of low methane concentrations in the vortex made by the HALOE instrument on board the Upper Atmosphere Research Satellite. ¿ American Geophysical Union 1993