I learnt that an adjective clause or relative clause contains a relative pronoun (who; which, whose, whom, that), or a relative adverb (when, where, and why)... is this correct? If yes, how can one then identify an adverbial clause?
The items "when", "where" and "why" introduce adjuncts (adverbials) of time, place and reason respectively:
ADJUNCT OF TIME: "I remember the day [when you were born"].
ADJUNCT OF PLACE: "I like a place [where you can relax"].
ADJUNCT OF REASON: "I know the reason [why she got angry"].
In each case, the underlined relative word functions as an adjunct, and adjuncts like these can be typically thought of as preposition phrases, so we get:
"I remember the day" + "you were born on that day" = "I remember the day when you were born".
"I like a place" + "you can relax at that place" = "I like a place where you can relax".
"I know the reason" + "she got angry for that reason" = "I know the reason why she got angry".