Learn Croatian: Došavši na potok, vidio je neki veliki grumen u vodi. - Having come to the stream, he saw a certain big nugget in the water.

Došavši is the past verbal adverb, meaning "having come." It's built from the perfective verb doći (to come). To form it, you take the masculine singular past tense form (došao), replace the final -o with -av, and add -ši. It is used here to show that the action of arriving was completely finished before the main action (vidio je - he saw) took place.

Could I just say "Kad je došao..." instead of using došavši?

Yes, absolutely! Saying Kad je došao na potok... (When he came to the stream...) is actually much more common in everyday spoken Croatian. Forms ending in -ši like došavši are mostly used in writing or formal storytelling to smoothly connect two actions performed by the exact same subject.

Why do we use the accusative case for na potok but the locative case for u vodi?

It comes down to motion versus static location. Na potok is in the accusative case because the action involves moving towards a destination ("coming to the stream"). U vodi is in the locative case because it describes where the nugget is statically sitting ("in the water") without any movement towards it.

Why is neki used before veliki grumen?

While Croatian doesn't have indefinite articles like the English "a" or "an," speakers often use neki (literally "some") to introduce a new, non-specific thing to the listener. Here, it acts a bit like saying "a certain big nugget" or just "a big nugget."