I've read here on Aviation SE that the aerodynamics of winglets on an aircraft are easily described as "extending the airfoil". Thus, as I understand it, a winglet is like stretching the airfoil a few feet and "bending" it upward.
Now, this answer mentions the various types of winglets used in contemporary aircraft, but I'm not sure the B737-800s I've seen (such as the one in the below image) with double winglets perfectly matches any of those categories1.
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?
1 I claim that the 737-MAX's "split scimitar" as mentioned in fooot's answer is different than the aftermarket double winglet seen in the United (Continental) B737-824 in the image.