Well, I'm sure you have excellent google abilities, and I don't want to be doing your homework for you, but I'll offer a couple of comments and cautions:
The NASA quote above is poorly written at best. I cringed at a few points when I read it. I don't know for sure, but it looks like they're talking about something a bit different than what you're interested in. There have been attempts (many of them successful) to reduce drag by making very small vortex generators all over the skin of an aircraft, car, or swimmer. However, none of these other than the "shark suit" for swimmers is in production. The thing that you're likely being asked to comment on is the series of largish vortex generators or possibly vortex generating tape (zig-zag stuff) that is usually placed just upstream of control surfaces such as ailerons.
Without going into any detail, the vortex generators create horizontal vortices which pull the fast, high energy air away from the wing down into the slow, low energy air in the boundary layer, re-energizing it. The faster air can make it around corner's better without separating from the wing. The result is that at high angle of attack, your ailerons are still effective. Without the vortex generators, the air could separate from the ailerons and you'd get a lot of drag without a lot of lift and lose roll control. (Slots in flaps do exactly the same thing, injecting air from below the wing into the boundary layer above the wing so that you can get large flap deflections without separation.)
Winglets are all about the wingtip vortex and induced drag. You're going to get a wingtip vortex no matter what (you wouldn't have lift without it), but if you can effect it's location and structure, you're ahead of the game. As Scott said, winglets mimic a larger aspect ratio wing. And as he pointed out, winglets need to be carefully designed. Well designed winglets will use the swirling air of the vortex to actually produce lift in the forward direction (thrust) to cancel out some of the induced drag.
Some people will tell you that the winglets block the air from below the wing getting to the top of the wing and producing a wingtip vortex. This is a major over-simplification and isn't really the case. Notice that winglets tend to have an airfoil shape and aren't just boards bolted to the ends of the wings.
You may also want to note that winglets are quite controversial in aerodynamics circles. They do reduce induced drag, but many argue that the better option is to simply increase the wing span by the same amount. Instead of having a 20' wing with a 1' winglet sticking up the top, you could just have a 21' wing and come out ahead. There are three major reasons that winglets are used:
1) If you have a wingspan which is fixed (gate restrictions, competition rules in gliders, or whatever).
2) You are upsizing an existing aircraft to make a new model and it's easier to bolt on a winglet to the existing wing than redesign the wing.
3) They look cool. This is the one that annoys engineers. I have talked to senior engineers at both Boeing and Bombardier who tell me that they were informed by the marketing department that they would have winglets because modern aircraft have winglets. No other reason.
Once you've had a chance to dig into the research end of things a bit, feel free to post or PM any specific questions or things that you find confusing and I'll help if I can.
Chris
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