Crossword Genius

Go up river (4)

Ross

I believe the answer is:

burn

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This clue could be a double definition.

'go up' is the first definition.
The answer and definition can be both acts as well as being singular nouns.
Perhaps there's an association between them I don't understand?

'river' is the second definition.
(thesaurus)

Can you help me to learn more?

(Other definitions for burn that I've seen before include "Scottish stream" , "Combust" , "Scottish brook" , "Scorch - stream" , "Heat injury; stream" .)

I've seen this clue in The Sun.
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