>Nuclear power is used to generate electricity which in turn powers electric motors.

Not always. Often, a PWR (pressurized water reactor) is used with a closed loop of superheated water that turns water into steam in a heat exchanger in order to directly drive propulsive turbines which are geared directly to the screws.

For example, the USS Tullibee was the first US submarine to use turbo-electric drive like you're thinking of, all of the other nuclear submarines before it used direct drive.

And almost all of the submarines afterwards. The Los Angeles class, for example, has the turbines connected physically to the screw, as does the current Virginia class subs (connected physically to the pumpjet).

In fact, I don't think the US has any nuclear powered ships that use turbo-electric propulsion. I know the Royal Navy does, though.