The effects of ambient turbulence on decay and descent of aircraft wake vortices are studied using a validated large eddy simulation model. The decay rate of the vortex circulation increases clearly with increasing ambient turbulence level but decreases with increasing radial distance, which is consistent with field observations. The decay rate of a pair of vortices is much larger than that of the single vortex. Simple vortex decay models are proposed as functions of dimensionless turbulence intensity (e0) and radial distance. A Gaussian type of vortex decay model can be applied at larger radial distances, while an exponential type of vortex decay model can be applied at smaller radial distances near the core, but the latter can be extended up to a radial distance of about half of the initial vortex separation distance (b0) for strong turbulence. The model coefficients are found to vary slightly with e0 and radial distance except for the extreme cases with very strong and very weak turbulence levels.
The circulation averaged over radial distances from 2.5 r0 (r0 is the initial core radius) to 0.5 b0, which is related to the rolling moment of an encountering aircraft, shows a Gaussian decay for weak and moderate turbulence and an exponential decay for strong turbulence. A model for the vortex descent as a function of e0 based on the vortex decay model is also proposed as a function of e0 and dimensionless time. The decay model for the average circulation has been applied to available field experimental data. In the absence of direct measurement, e0 can be estimated from the atmospheric boundary layer similarity relations.
The model predictions appear to be in reasonable agreement with observation data which have a large scatter, as long as the theoretical circulation is used as the initial value. The decay rates of observed circulations are much larger than those obtained from our numerical simulations, impling that besides ambient turbulence there are some additional factors enhancing the vortex decay. In particular, the effect of ambient stratification on the enhancement of the vortex decay appears to be significant