Prophetic recent letters dispatched from nuclear reactor meltdown (8)
I believe the answer is:
oracular
'prophetic' is the definition.
(similar in meaning)
I can't explain the remainder of the clue.
(Other definitions for oracular that I've seen before include "In the manner of one possessing divine wisdom" , "To do with advice or prophecy as from ancient Greeks" , "Prophetically ambiguous" , "like Mrs Malaprop's tongue" , "Auspicious" .)