A better answer maybe that United believes that a cruise performance boost of 30-40% is worth the effort.

Thus, my question is: How can one best describe the aerodynamics (and benefits) of the second, downward-pointing winglet in the context of airfoil extension?

You can extend the wings many feet which reduces drag and also makes for a very ramp unfriendly airplane. Winglets make wings behave as if they where longer. Wingtip vortices are reduced with the one upward winglet the lower or downward scimitar tip reduces vortex loss even more.

Hope this helps.

A reasonably complex question. What you see is call a Split Scimitar Winglet. Lots of references online – see Wingtip device on wikipedia. Simplest explanation: "Their intended effect is always to reduce an aircraft's drag by partial recovery of the tip vortex energy."

A better answer maybe that United believes that a cruise performance boost of 30-40% is worth the effort.

Thus, my question is: How can one best describe the aerodynamics (and benefits) of the second, downward-pointing winglet in the context of airfoil extension?

You can extend the wings many feet which reduces drag and also makes for a very ramp unfriendly airplane. Winglets make wings behave as if they where longer. Wingtip vortices are reduced with the one upward winglet the lower or downward scimitar tip reduces vortex loss even more.