The effective diffusion of aircraft emissions and the growth of plume cross-sections at cruising altitudes of commercial airliners are examined by means of large-eddy simulation in a domain of size 4.3¿1.1¿1.1 km3. It is assumed that aircraft-induced turbulence has ceased and that the exhaust plumes can be represented by line sources with Gaussian cross-sections. On the basis of a previous study where the effective diffusion in a stratified atmosphere with negligible wind shear was investigated <D¿rbeck and Gerz, 1995>, the work is extended here to situations with shear rates typical for the free atmosphere ranging between 0.001 s-1 and 0.007 s-1, covering bulk Richardson numbers Ri between 0.13 and 360. Along a flight track the atmosphere is usually only weakly turbulent (Ri>1); an aircraft encounters strong but highly intermittent turbulence (Ri1, shear has no significant influence on horizontal or vertical effective diffusivities which lay, for a stratification of 0.019 s-1, in the range of 15 m2 s-1≤Dh≤23 m2 s-1 and 0.15 m2 s-1≤Dv≤0.18 m2 s-1, respectively. But shear in combination with diffusion enlarges the cross-section of an exhaust plume and increases the entrainment rate. When Ri≈0.1, the diffusivity Dh grows by a factor of about 3 and Dv by a factor of about 20 compared to shearfree situations. With increasing shear and time, only Dv and shear control plume sizes and entrainment rates, whereas Dh has a diminishing influence. The results agree very well with data from recent in situ flight measurements in the North Atlantic flight corridor in the tropopause region. ¿ American Geophysical Union 1996