Actual answer:
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This is Figure 7-9 in NIST NCSTAR 1-5A. Sourcing is given in the report.
The lighter vertical feature at left of WTC 2 is a vortex core, made visible by entrainment of dust, debris, smoke, and atomized fuel thrown off at impact. This vortex core is a result of the aircraft wake -- indeed, there is no other plausible source for this artifact.
Having said that, the photography of the WTC 2 impact is much less clear than it was for the first, WTC 1 impact. This is because WTC 1 was already burning and creating a very complicated flow pattern due to its thermal plume. By contrast, the first impact happened in relatively stable and calm air, and for it we have extremely good photographs of the resulting vortex:
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Figure 6-2 from NIST NCSTAR1-5A
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Figure 6-3 from NIST NCSTAR1-5A
I imagine that everyone is looking for something that looks like a "wingtip vortex." This is a mistake -- you're not going to find that. The wingtip vortices are in fact a rather minor part of the aircraft wake. The only reason they're familiar to us is because under normal conditions, they're more likely to become visible. The wingtip vortices are much more organized and predictable than the entire wake. But they're small by comparison.
What exactly is the "wake?" The wake is the flow disturbance behind a moving body, and that goes whether the body has wings or not. Think of a large bus barreling past you: You'll feel a gust of turbulent wind as it passes, even though there are no wings and thus no wingtip vortices. This wake is simply a region of entrained air, a mixture of air accelerated along by the body and the complex mixture of vortices shed off of the body, of which the wingtip vortices are only a part.
For an aircraft, the wingtip vortices are also relatively weaker as the aircraft goes faster. This is because these vortices are directly related to circulation around the wings -- in other words, lift -- and lift remains roughly constant with speed, since the weight of the aircraft isn't changing. The rest of the wake, on the other hand, corresponds to drag. Drag does change as the aircraft speeds up, it in fact scales as the velocity squared. On top of this, the wingtip vortices appear weaker at higher speed because, as speed increases, the total circulation stays the same, but it's spread out over a longer distance per unit time.
Since both of the crashing aircraft were moving rather quickly, we therefore do not expect the wingtip vortices to be much of a factor. The overall wake will be dominated by the entrained air.
Now, what about those shapes? Especially in Figure 6-3 above, what we see is a
vertical vortex core (actually a pair of them). How does this happen?
Well, this arises because the entrained air is smacking into the building, just like the airplane did. But unlike the airplane, this air is relatively inviscid and carries less inertia. Instead of punching into the building, the wake instead flows around the sides of the building. It can't flow below it because the ground is there, and it mostly won't flow over the top because the buildings are much higher than the impact. So we see the wake split into two turbulent jets, each turning around the sides of the structure.
When they do this, they acquire
vorticity. Now, vorticity is conserved just like any other angular momentum, so as the wake sheds from the building, it is rotating in large scale. This generates a so-called "vortex core," just like a dust devil. The rotation also serves to contain the dust and smoke that got mixed in at impact, so as the vortex core moves away from the structure into clean air, we can still see it for a little while.
The vortex core also tends to stretch vertically, and gets thinner as it does so. This is because the vortex will have some vertical velocity dispersion and will ingest more surrounding air, not to mention having now falling objects within it entraining some air downward, and fire nearby causing an updraft. But remember that the total vorticity is conserved, thus as it grows, it slows. This is achieved by a smaller diameter of the core.
All the while, the vortex core will be losing some of its rotation by creating eddies in the surrounding air, and eventually it will no longer be stable, dissipating into pure turbulence. But we can see it for several seconds after impact, as the photographs demonstrate.
There is no mechanism, other than entrainment by a fast-moving object, for these wakes to form. Not unless there was a ten-story
Airzooka on the WFC that we all missed.
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This is an extremely minor footnote and of no practical value in understanding September 11th, but since every single person in the thread got it wrong, I figured it was worth an explanation. Airzooka, incidentally, generates a ring vortex, which is not the same kind as the ones in the photographs.