Erdal (2004)
A Grammar of Old Turkic
p. 395-396
kudï governs the nominative in säläŋä kudï ‘down the Selenga (river)’ in BQ E37 and ŠU E4, but the locative or (more often) the ablative in the rest of Old Turkic. kudï comes from kud- ‘to pour’ because liquids move downwards, including the river mentioned in this example. The contexts in question thus show the word in its original function, and we do not know whether it retained its government of the nominative once its use was extended to cover downward movement in general.