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The decayof wing-tip vortices under the inè uence of turbulence in a stablystratié ed atmosphere is discussed by means of large-eddy simulations. The vortices originate from a B-747 aircraft in cruise. Atmospheric turbulence and turbulence originating from the boundary layer around the aircraft are distinguished. The former is weak and anisotropic with eddy sizes in the order of the wing span, whereas the latter is wrapped around the vortices with the maximum intensity at the core diameter. During their descent, the parallel vortex tubes approach each other because stratiécation and turbulence detrain mass into the ambient air. The atmospheric eddies deform the trailing vortices such that their spacing varies. This, in turn, yields different mutually induced velocities that amplify the deformation quickly according to Crow's instability theorem. The bent vortex tubes link after about 1.5 min and form rings. The continuous trail of turbine exhaust is reorganized in a row of single puffs. Without any atmospheric turbulence the vortices approach each other but remain parallel. They start to dissolve after 2 min when they touch. This dissolution is triggered by the small-scale boundary-layer turbulence. The exhaust trail remains aligned along the èight track. HE life cycle of the aircraft wake and the exhaust jets is con- veniently divided into three phases: During the jet regime, the exhaust from the turbines is entrained into the two counter-rotating wing-tip vortices, which at the same time roll up from the sheet of vorticity around the wings. In the following vortex regime the vor- tex pair propagates vertically downward by mutual velocity induc- tion. Most of the exhaust is stored in that primary wake and, hence, also sinks below è ight level. However, as the primary wake moves downward it produces a wake itself, the so-called secondary wake, because the baroclinic force leads to detrainment of some of the ex- haust and leaves a thin curtain of exhaust above the sinking vortex pair.Turbulentmixingincreasesthatdetrainment.Thevortexregime is followed by the dissipation regime when the organized wing-tip vortices break up into an unorganized (turbulent) wake è ow and its energy dissipates to the background level. In that phase the highly concentrated exhaust in the primary wake is suddenly released and diffuses quickly.1 Although the principal processes controlling the life of such vortices and the distribution of the turbine exhaust are wellknown,theeffectofturbulenceatvariousscalesuponthedecay process is rather unclear and joins the role of stable stratié cation. Both are still subjects of controversy in the literature.2-7 Turbulence originates inherently from the unstable vortex sheet behind the trailing edge of the wing, including turbulence from the boundarylayeraroundtheairplaneandfromtheexhaustjets.Turbu- lence also is often a è ow state of the surrounding atmosphere. Both kinds,however,differconsiderablyinstrengthandlengthscale.Mo- tivatedbytheneedtoassesstheimpactofaircraftemissionsuponthe atmospheric state and climate, we consider an ambient èow typical for the height of the tropopause where airliners cruise. There, local zones of wind shear of breaking gravity waves cause turbulence,8;9 which is anisotropic and very spotty in space and time. Moreover, the atmosphere is stably stratié ed at that height most of the time. Inthisstudywewanttoinvestigatehowturbulenceofbothsources (from the aircraft and the atmosphere) affects the decay of the vortex system behind a cruising aircraft in a stably stratié ed en- vironment. The aircraft under consideration is a B-747. We utilize the method of large-eddy simulations (LES). Similar studies have been undertaken10 but without discrimination between boundary- layer and ambient turbulence. In a previous paper11 the vortex-è ow

Wing-Tip Vortices, Turbulence, and the Distribution of Emissions