On the other hand, increasing to three carrier strike groups would be noticeably more 'robust', belligerent and suggestive of intending or anticipating attack. The difference between two and three strike groups is huge. Two ='s strong and capable, but existing offensive intent is less probable; three ='s 'we don't care about provocation, we're preparing to fight in this new dimension'.
(An indicator would be to watch for announcements about Nimitz strike group; Nimitz reportedly has completed the routine pre-deployment work-up and is in San Diego.)
The US has eleven carriers (with #12 on the way). Sending three out of eleven to the Gulf is more than saber-rattling.
Worse, the Gulf is too small for three carrier groups to function effectively, and has one entrance/exit that is about 20 miles wide and runs along the Iranian coast. This creates a sitting duck effect — a 'target rich' environment for potential attackers. In other words, it's inviting Iran to take the bait, something that becomes increasingly likely the more that the Iranians come to believe that they are about to be attacked. (Which is undoubtedly the point of the US government media strategy.)
Gulf of Tonkin meet Persian Gulf.