sigh-a-thon 

Def- the repetitive release of sighs in lieu of actual words used to passive aggressively attempt to communicate: frustration, resentment, contempt, anger or some other feeling that grows inside when one has swallowed their words and silenced their truth. Used almost exclusively by folks who aren't even aware how disconnected they are from authenticity.

auditory passive aggression

He said nothing, just gave a lengthy sigh-a-thon. Who knows how he felt about my new job.

no conversation silent treatment with sighs

sigh-a-thon by Dasharona Long April 19, 2018