I agree with Seagull's explanation.
Many problems in physics can be explained using different theories, but ultimately they all tie back "to the basics" - Newton's laws. One example is looking at motion using the conservation of energy approach, or the mass-force-acceleration approach. The answers come out the same.
Now, on to vortices. Whenever lift is produced, there must be "circulation" component around the wing. This is more mathematical than physical, but the if you want to imagine it physically, assume that superimposed on your streamlines around the wing is another component of circular streamlines. The resultant streamlines are obtained by adding the two together. This is accomplished by adding the stream functions of each set together, point by point, and joining points of equal stream function together to get the streamlines. The strength of this circular component is adjusted (mathematically) to skew the resultant streamilines so that the stagnation points fall at the leading and trailing edges in the actual (physical) locations. This circulation, mathematically, is equivalent to lift.
However, there is a physical manifestation of circulation, and that is vortices. These are generated whenever there is lift. Vortex shedding has been a challenge from the early days. There are many schemes for controlling it, and I would assume from the posts above that the winglets may be another tool for this.
Regardless of how you explain it, ALL equations and principles of physics apply to winglets, be it Bernouli, Newton, etc.
I know this sounds complicated in words, maybe one day I will make some sketches and post them on a website.
"In God we trust, everyone else bring data"