The transport and effective diffusion of exhaust are analyzed in the wake flow of a large-bodied aircraft which flies through a stably stratified, sheared, and turbulent atmosphere. The analysis is based on data sets from large-eddy simulations of the wake in the atmosphere. Diffusion and dilution measures are obtained from a chemically inert species concentration. Most of the exhaust is concentrated and isolated in the two wing tip vortices (the primary wake). However, as the vortices sink through a stably stratified atmosphere, a baroclinic torque develops between the vortices and the surrounding flow and detrains about 10 to 30% of the exhaust mass from the vortices into the ambient air (the well mixed secondary wake). Consequently, the entrainment rates computed for the primary and secondary wakes differ by orders of magnitude. In the period between 1.5 and 3 min the vortices collapse into aircraft turbulence. The trapped emissions of the primary wake are now released and diffused by ambient turbulence and shear. After about 5 min the exhaust concentration has been diluted by 2¿10-5 and 4¿10-6 compared to the value at the nozzle exit for the primary and secondary wakes, respectively, and covers areas of about 5¿104 m2 and 2¿104 m2. Under flow conditions typically found at cruising heights the emissions are diluted to background concentrations within 2 and 12 hours for wind shear between 0.002 and 0.01 s-1. The spatial plume extension does not exceed the lower mesoscale range (20 km horizontally and 0.3 km vertically). Good to excellent agreement is achieved between the numerical results and in situ measured data. ¿ 1998 American Geophysical Union