Why were these Hawkeyes flying in a circular pattern?
They were most probably training touch-and-go passes. USN conducts carrier landing practice at NASA's Wallops Flight Facility for E-2 Hawkeyes and C-2 Greyhounds.

As Lt. Commander Mike Ferrara, an operations officer with the Navy's Carrier Airborne Early Warning Squadron 120 (VAW-120) explains in this article:


  These two aircraft are very difficult aircraft to fly — that's why, when we're up here, you'll probably see us going around for three hours at a time, take a break, and go for three more hours ...