There are 2 common articulations of /r/ and /r̩/ in American English, one retroflex, and the other dorsal. This phone is called the molar or bunched r. It can be described roughly as a back-palatal or pre-velar approximant that's somewhat bunched up along the left-right axis, and it's often labiodentalized when syllable-initial. RainDoctor cites John Laver as describing it as a "voiced labial pre-velar approximant with tongue-tip retraction".
I've been transcribing it ad-hoc as ⟨ɰᶹ˞⟩ or ⟨ɨᶹ˞⟩, using ⟨˞⟩ as an attempt to indicate the bunching that imparts the characteristic sound.
But this seems like an abuse of notation, and it doesn't specify what the articulatory change is that makes it rhotic; is there a standard way to represent this phone?
(Asking on Linguistics since it's not about the sound per se, but about the notation for transcribing it.)