The act of a member of
the Royal Family waving at a member of the public but not in a Royal style (hand
rotating in a forward direction with fingers fixed at a
horizontal angle) but with their hand and fingers pointing to the person and them moving their fingers up and down in a friendly manner just like they are waving at an acquaintance.
In 1982 the Queen Mum
waved at me with a Royal Finger Wave and not the usual
Royal Wave whilst I crossed a bridge
over the River Thames in London with my father.