This is listed by Wikipedia as a "common" type of wave:
Another common wave is to raise one's hand and repeatedly move the fingers downward toward the palm.
Wikipedia also seems to suggest that this style of wave originated in Europe:
Waving the hand to say "hello" or "goodbye" [in Europe] is done by moving the fingers down towards the wrist and back to an open palm position while keeping the palm facing out.
It's worth noting that almost all White Americans are descended from European immigrants in some fashion. This explains why a) the gesture sometimes appears in American pop culture, and b) viewers from outside Europe and North America (such as yourself) may not recognise this style of waving.