Crossword Genius

Greek river becomes blocked, by the sound of it (4)

Ross

I believe the answer is:

styx

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'greek river' is the definition.
'styx' can be an answer for 'river' (mythical river). I'm unsure of the 'greek' bit.

I cannot understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for styx that I've seen before include "Underworld river ferried by Charon" , "River Charon rowed on" , "Hellish current" , "The last river one crosses" , "Hell's river" .)

I've seen this clue in The Independent.
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