How turbercle wings could generate aerodynamic advantage?
No, please, not another revolution of how we build airplanes again!

The linked article mentions two guys who pose as the discoverers of humps on whale flipper leading edges. What precisely have generations of marine biologists overlooked before?

Now to the humps: They produce a 3D flow pattern close to the leading edge which will help the flow to transition to a turbulent boundary layer more quickly. This is helpful at high angle of attack at intermediate Reynolds numbers (around 1 Mio) and will make the whales more maneuverable.

This is not to say that it will help any existing aircraft. Had nature given the whales the opportunity to integrate slats and double-slotted flaps into their flippers, they sure would have done so. This will help much more to increase maximum lift. Also, typical aircraft Reynolds numbers are much higher than those on whale flippers, and there turbulent transition is very quick. Right now, most efforts center on delaying this transition to reduce friction drag.

Swept wings will see a massive drag increase if this sort of leading edge is used.

The "tubercles" are a very specific form of turbulators and optimized for a narrow application. In other words, don't invest in this WhalePower company!