Currently, there is quite a bit of research going on relating to the vortices, mostly for reducing spacing on final to increase capacity.
The research is changing the understanding of the mechanics of vortex creation. There are volumes of documentation from the the WakeNet-USA and
EU WakeNet studies.
Enroute vortex generation is important for fuel savings, but currently, the research is really driven by the military and mid-air refueling operations, and most recently, for unmanned tankers fueling unmanned platforms.
NASA just completed the formation flying with 7 C-17's flying in formation. he attempt was to keep the trailing ac in the uplift part of the rollup of the leading vortex. Over the course of a 5 hour flight, they noticed that the trailing aircraft had to re-position several times to stay in the uplift portion, because the leader vortex was changing as it lightened up and the AoA changed.
For final approach, the more measurements that are being taken, the more the concept of wake generation is changing. One can look up the research and see the images, many of them just a simple wing section extruded in length. This was about all the modelling that could be accomplished, and the concepts regarding wake generation were the result.
There was no impetus to model an actual wing section, change weight and/or angle of attack, and no way to even consider different flap settings. The wing designers and others completely discounted, (and in fact, some still continue to discount) the flap settings.
As a result, winglets were originally marketed as reducing wing vortex generation, thus reducing drag. Airbus did extensive studies with the A380, in an attempt to get the wake sep behind it reduced. They found that the winglet configuration had no effect on vortex generation.
So in regards to winglets, the boundary layer is very sensitive to pressure changes. With the wing taper, as the pressure rises, the boundary layer begins to shift towards the leading edge, leading to turbulent airflow at the trailing. This is the drag that reduces fuel effeciency. It is somewhat easy to envision a wing section in flight, at the beginning, with a higher AoA, that the transitional area would be much greater, than as the ac AoA lessens with reduced weight.
The winglets, at these angles of higher AoA, effectively move the transitional area outwards, increasing the boundary area of laminar flow, the reduction of turbulent flow is less drag, therefore better fuel economy under those conditions. The lower drag economy outweighs the increased friction drag of the winglet itself.
Boeing decided to use the large radius winglets to mitigate boundary separation with the pressure differential at the corner. This lead to a very tall winglet, and the associated friction component.
Airbus decided to use the right angle winglets, and to mitigate this, the leading edge of the winglet is moved into the region of the pressure rise of the wingtip, with the winglets pressure rise region moved behind the wings trailing edge. This places the winglets in a region where the pressure gradient mitigates the wings pressure rise.
more later....