Answer: The word that functions as an adverb in the sentence is "closely".
Step-by-step explanation: An adverb is a type of word used to modify a verb, an adjective or another adverb. Moreover, adverbs usually refer to the circumstances in which an action develops and they generally end in "-ly". In the sentence provided, there is a word that functions as an adverb: "closely". "Closely" is an adverb because, besides ending in "-ly", it is modifying the verb "watches". Furthermore, "closely" is providing information about the way in which the subject ("she") is carrying out the action.