Dispersion of aircraft exhausts in the free atmosphere

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Abstract
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 [Dürbeck 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 (Ri < 0.25) only occasionally. Both situations are examined here. It is found that when Ri > 1, 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 m2s−1 ≤ Dh ≤ 23 m2s−1 and 0.15 m2s−1 ≤ Dv ≤ 0.18 m2s−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.