If you look at the colors while circling, the aircraft was ascending and descending. The E-6B pilots require landings to remain or become qualified, so they do touch-and-goes. That's extremely common for that aircraft. The E-6 does not have observational capabilities, meaning no infrared or radar to monitor ground activities. They do have a color weather radar, but that's for looking up/out, not down at the surface. Circling overhead gives that aircraft no advantage to "see" anything going on unless they were low enough to see with their eyes.

Looks like a very routine flight and not an exciting one at all. They didn't even get out over water to transmit VLF to the subs.