Compared to a nuclear factory, the nuclear power generator in a warship is tiny. It’s also very well protected because if there were to be a breach in the nuclear generator, it would be catastrophic for the vessel. It’s basically a core of radioactive material, which gives off heat, and that heat is turned into electricity. So basically, it’s quite possible and even likely that a vessel of this type will have a catastrophic accident, and sink, without damaging the nuclear core, which is probably the most protected part of the ship. The nuclear cores are incredibly strong. It will probably degrade over time and eventually fail, but that will probably take a century or more if it’s intact when it sinks. At that point it’s at the bottom of the ocean and there isn’t enough radioactive material to cause an issue.
If it is indeed sunken in a port or shallow waters, the navy would most likely extricate the nuclear core. But like I said, it’s a relatively small amount of nuclear material so in most cases, it wouldn’t be catastrophic.
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