1999 CONFERENCE ON THE ATMOSPHERIC EFFECTS OF AVIATION (April 18 - 23)
EFFECTS OF AIRCRAFT WAKE DYNAMICS ON CONTRAIL DEVELOPMENT
by D. C. Lewellen and W. S. Lewellen
In response to many requests, here are slides from our 1999 AEAP presentation along with some notes. The corresponding paper is in preparation, but its completion date is uncertain, as we are still conducting simulations. Any comments or questions can be addressed to us via email.
Some brief notes on the slides:
Title slide: As part of a larger effort to assess the potential impact of aircraft traffic on the environment, we focus here on the question of whether the aircraft wake dynamics occurring from a few seconds to tens of minutes behind the aircraft has any lasting effects on the resulting contrail.
The second slide gives a brief model overview. Details can be found in Lewellen and Lewellen AIAA Journal, Vol.34, pp.2337-2345, 1996, and Lewellen, et.al., AIAA Journal, Vol.36, pp.1439-1445, 1998.
The third slide gives some idea of the different conditions used for the simulations.
Slides 4 and 5 illustrate some of the basic wake dynamics out to a time of 5 minutes for a B747 with large ambient ice saturation (130% relative humidity with respect to ice). The format is as described in Lewellen, et.al. 1998. The horizontal axis in each case varies over time as well as downstream distance so that both the temporal evolution and spatial structure can be seen. Slide 4 is a view from below with the fields vertically integrated; the low pressure centers in the second panel provide a good view of the trailing vortex dynamics. Slide 5 is a view from the side with the fields integrated in the cross-stream direction. Initially the vortex pair falls rapidly downward. Perturbations of the vortices from the ambient atmosphere grow in a sinusoidal mutual inductance instability (the Crow instability). Eventually the vortices touch, reconnect and form vortex rings which oscillate, interact with themselves and the atmospheric turbulence and stratification, and finally dissolve. During their lifetime the rings continue to drop, giving rise to the periodic series of puffs often seen in contrail evolution (slide 6).
At this large value of ice supersaturation the ice crystal number density behaves like a passive scaler. The ice mass, meanwhile, grows with the volume of the plume as moist ambient air is mixed in. Slide 7 shows a downstream space/time slice (rather than the cross-stream integration as in slides 5 and 6) for the same case. The mean crystal diameter in the bottom panel shows the expected inverse relationship between crystal size and number density. The ratio of the actual ice mass to the local equilibrium value in the top panel show that the ice plume is in general close to equilibrium everywhere. The exceptions are the plume edges, where the crystal numbers fall off, and, more interestingly, in the rapidly falling vortex system. As the fluid around the vortices falls it is adiabatically compressed by the increasing ambient pressure level. The accompanying rise in temperature lowers the relative humidity in this fluid so that the existing ice mass is above the now lowered equilibrium level. At high ambient humidity levels this effect has no lasting consequences; however, for more modest ambient humidity this is no longer the case as illustrated in slide 8. The conditions are the same as before except the ambient relative humidity with respect to ice is now 110% (and 10min. of simulated results are shown). The compressional heating now leads to the eventual evaporation of the ice crystals within the immediate vicinity of the vortices. This effect was first noted in the literature by Sussmann and Gierens (GRL, 1999) in the context of two dimensional simulations with very low ambient ice supersaturations. In three dimensions we can carry the simulations past the vortex linking stage to find that this can be an important effect even for significant ambient ice supersaturations. The evolution of the actual ice crystal number density is now quite different than that of a passive tracer (top two panels).
The fraction of ice crystals lost through this mechanism depends on a competition between the rate at which the fluid around the vortices is forced below the saturation level (and the ice crystals sublimate), and the rate at which moist ambient fluid is mixed into this system. Slide 9 illustrates results analogous to those in slide 8 but for a B737. In this case with a smaller aircraft (whose vortices fall neither as far nor as fast) the ice crystal loss is much less, and the contrail retains the full plume volume.
Slides 10 and 11 summarize some results from several of our simulations to date. The increase in total ice mass along with the fraction of ice crystals surviving is evident as the ambient relative humidity with respect to ice is increased. More surprising are the differences between aircraft. While the B747 contrail has a larger total ice mass than the B737 for high ambient supersaturations, we have for RHice = 110% that the B737 eventually produces as significant a contrail as the B747 even though it consumes only about 20% as much fuel per meter of flight path. We note as well the drop in the fraction of ice crystals evaporated when the effective emission index for ice crystal numberis dramatically reduced; the slower rate of ice mass growth when the vortices are dominant; the increased ice mass at late times when significant cross-stream wind shear is included (S=.01); and the effect of Brunt-Vaisala oscillations of the wake plume at later times.
Slides 12 and 13 are a side light, dealing not with ice physics but with some effects of species fluctuations on chemistry measurements in the aircraft wake. Slide 12 is a figure from Tan, et.al. (GRL, Vol.25, pp. 1721-1724, 1998) showing HOx measurements taken during the SUCCESS campaign. The circles are measured HO2/OH ratios, the plusses are what one would expect theoretically assuming local equilibrium of HO2 and OH (as seems reasonable given the fast reactions governing these concentrations in the plume). These measurements were all 1 second samples, during which the sampling aircraft travels of order 200m. As is clear from previous slides there are significant species fluctuations on such length scales in an aircraft wake. Our simulation results in slide 13 suggest that the discrepency between measurement and theoretical expectation in slide 12 may be due entirely to the effect of averaging over these species fluctuations (in particular the dramatic difference in HO2 concentration inside and outside of the wake plume). Here we have shown results of a B757 simulation including simple NOx, HOx, and ozone chemistry. We have not yet tried to match with the SUCCESS flight conditions in detail. We have assumed local equilibrium of HO2 and OH in obtaining these results. The scattered points are from 1 second averages collected in analogy with the observational data; the black line the equilibrium ratio. The different colored points represent different ages of the sampled wake; the distribution is strongly affected by the growth of the Crow instability for the samples shown.
Slide 14 summarizes a few of our conclusions. We note in particular that because of (4) the assumption often made that the ice mass in a contrail for given ambient conditions is proportional to fuel usage is not supported by these results.
