Learn Farsi: من چرخش آب در رودخانه را تماشا کردم. - I watched the swirling of the water in the river.

چرخش is made from the present stem of the verb چرخیدن (to turn or spin), which is چرخ. When you add the suffix ـِش (-esh) to this present stem, it creates the action noun چرخش, meaning 'the act of turning' or 'swirling'.

Why is the direct object marker را placed after رودخانه (river) instead of right after چرخش آب?

In Farsi, when a direct object is modified by a prepositional phrase like در رودخانه (in the river), the را often moves to the very end of that whole descriptive chunk. Here, it marks the entire phrase 'the swirling of the water in the river' as what you watched.

Is there a hidden sound connecting چرخش and آب?

Yes, there is an unseen ezāfe connecting the two words, pronounced as charkhesh-e aab. It acts like the English word 'of', linking the action noun 'swirling' to 'water' to mean 'the swirling of the water'.

I know the verb for 'to watch' is تماشا کردن, but what kind of word is تماشا on its own?

On its own, تماشا is a noun that means 'a spectacle', 'a view', or 'watching'. Farsi builds many verbs this way: combining a noun like تماشا with a 'light verb' like کردن (to do) to create the action.