Phrasal verb with "turn "

Fill in the blank
"She was standing at the end of the pier looking out to sea and I waited for her to turn _______ so that I could see her "

I am confused by “turn a(round)” and “turn up” so please clarify them
Also, I would like to be made clearly about “turn away” and “turn down” as they both have the meaning “to refuse sth”

Thanks for help

Turn around = pivot 180 degrees.
Turn up = arrive
Turn away = refuse entry
Turn down = refuse an offer

Hi Mister Micawber ,
Thanks for help
So , no word above can match the sentence, right ?
Can you tell me the answer to fill in the blank ?

‘Around’ is the correct answer.