The fine‐scale structure in lower stratospheric tracer transport during the period of the two Arctic Airborne Stratospheric Expeditions (January and February 1989; December 1991 to March 1992) is investigated using contour advection with surgery calculations. These calculations show that Rossby wave breaking is an ongoing occurrence during these periods and that air is ejected from the polar vortex in the form of long filamentary structures. There is good qualitative agreement between these filaments and measurements of chemical tracers taken aboard the NASA ER‐2 aircraft. The ejected air generally remains filamentary and is stretched and mixed with midlatitude air as it is wrapped around the vortex. This process transfers vortex air into midlatitudes and also produces a narrow region of fine‐scale filaments surrounding the polar vortex. Among other things, this makes it difficult to define a vortex edge. The calculations also show that strong stirring can occur inside as well as outside the v