I cannot say what our top speed was. It was classified.
And in truth, even though I worked in engineering, I did not know. We don't have a speedometer in the control room (damn I can't remember the name of it). Basically you got the electrical panel, 2 reactor control panels (Enterprise class had 8 reactors- a bit redundent- but they were based off of submarine designs), and the main engine control pannel.
The orders came down from the bridge/pilot house. If they ordered all ahead flank, we gave it to them. But we had no idea how fast the ship was actually going.
That's about what I expected, but thanks for shedding light where you can. First of all, let me say that I've had a life-long fascination with aircraft carriers (since I was 7, I wanted to be the Captain of one - fell short however

). Basically, the best we can do is go by personal experiences, weighing some more heavily than others (i.e., my instructor I mentioned previously - I hold what he said in high regard, he worked in the tower/(island), and knew a sailors that worked on the bridge, including a helmsman), and try to piece things together.
Anyway, I've had the chance to know a lot of sailors/Marines that did various odd jobs on the Nimitz ships (ordnance, lift operators, aircraft mechanics, etc.) and they've all said the same thing... when the ship decides it wants to haul @ss, it's truly something to behold. Like Neptune himself is under the ship, pushing it through the water at an 'unnatural speed'. 60 knots comfortably. Anything more than that... and you're delving into speculation (difficult to be certain).
But, what speed would be necessary, in order to make the cutting of the water at the bow of the ship be such a large size/volume of water, that it would actually splash up onto the deck on a calm sea?
I knew another Navy air traffic controller (spent time on the ship), when we worked together in a tower as civilians. He didn't know the top speed either, but he had some stories that made me awestruck. But whatever - the ship itself is already impressive. I would just like to know what kind of accomplishments mankind is capable of, when it comes to propelling such a ship. A rough idea, anyway. But, it'll probably remain illusive. -Until I actually befriend a helmsman someday, that confides in me. It would be cool to know - but I do respect why it's classified information, and if I really knew, I'd keep it to myself..
We were talking about the F-15 earlier, btw. What it's top speed? "Mach 2.5+"

Always has been. That's all they'll ever tell us.