Fluttered (5)
'fluttered' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for waved that I've seen before include "Moved freely to and fro" , "had a flutter" , "Signalled by hand" , "Signalled with the hands" , "Waggled" .)
(Other definitions for hovered that I've seen before include "Hung in the air" , "Remained in the one place in the air" , "Remained in the air without moving" , "Floated" .)