According to most online resources, including NASA, induced drag is caused by wingtip vortices which induce downwash. However, in StackExchange I have found a few answers (Peter's and Jan's) that actually drag caused by vortices is a myth and induced drag is a simple inherent reaction force (vortices and induced drag are both consequences of downwash, which itself is caused by lift creation). Although this theory looks quite intuitive, I am still confused. Could anybody give me some links to more extensive research of this issue or explain which one theory is scientifically correct and why?
Oh, but they are all* correct!
First, we have to say that we are not talking about cause here. There is a flow around the wing and it has certain properties and neither is cause of the other; they are both effects of the flow. What we are talking about here is explanations why every flow that produces lift also produces induced drag.
And as far as explanations go, there can be more than one, because the physical theories have a lot of redundancy in them. You can usually arrive at the result by multiple ways.
You can use the orientations of the normals (the Peter's answer), you can use laws of conservation of energy and momentum (my answer) or you can use the potential flow theory and that explanation will indeed involve the wake vortices. Because the potential flow theory is a mathematical apparatus for analysing fluid flow as a combination of vortices and from that angle of view, the energy is indeed carried away by the wake vortices.
However, the wake vortex explanation has one problem: it is often associated with different misconception, the one that the vortices are caused by transverse flow around the tip and the resulting idea that it can be eliminated by doing something with the tips specifically.
But that's not what the potential flow theory says. According to the potential flow theory, there is a vortex originating from every point along the span and they combine to form the two tip vortices. So like the other explanations, it also clearly says the induced drag is related to any generation of lift. And if you understand that, it is correct. I still consider it unnecessarily more complicated.
* All the three you listed that is. The ones that claim the wingtip vortex is caused by transverse flow around the tip are not, because it isn't. The wingtip vortex is just the vortex line of the overall wake (and should preferably be called wake vortex).
$\begingroup$ Now explain it for helicopters. 8^D $\endgroup$ Nov 7, 2016 at 21:57
$\begingroup$ Aerodynamics is so simple when it's introduced this way. $\endgroup$– minsNov 7, 2016 at 22:18
$\begingroup$ @KorvinStarmast, the arguments apply to rotorcraft almost directly. The only difference is that the flow is due to rotation of the rotor instead of forward motion. But the lift generation works the same. $\endgroup$ Nov 8, 2016 at 5:55
1$\begingroup$ Thank you, Jan. It is getting more clear to me. But does it mean that winglets do not have any effect except for changing the aspect ratio a little bit? $\endgroup$ Nov 8, 2016 at 13:54
1$\begingroup$ @RokasZilinskas, winglets have a little bit of effect, but indeed not very big and there are better ways to reduce drag, so winglets are only used in upgrades to old designs, because they are easy to retrofit, or if the wing span is limited by other concerns. For more details, see this analysis by Peter Kämpf. $\endgroup$ Nov 8, 2016 at 18:13
which one theory is scientifically correctis that questions about induced drag / lift have the Blind men and the elephant problem. Just remember that any simple answer to a complex question will be at least a little bit wrong. $\endgroup$