Bsrgvty

There's a lot that goes into answering this, and the answer could turn into either yes or no depending on what assumptions and trade-offs you make.

Firstly, nuclear carriers have an operational lifetime of 50 years, and get a overhaul and refueling at the 25 year mark. This is assuming that the carrier is actively being used for military purposes, if you're content to let it float or cruise at low speed in the middle of the ocean, this timeline can likely be extended to a degree, however there will come a time when the nuclear plant has to be shut down because the lack of maintenance makes it too dangerous to operate even if you've still got fission fuel.

Second bit, there's a lot of stuff happening on an CVN that's just there to keep it in fighting shape: F-16s? Chuck 'em. Avgas? No need for that. Munitions? Garbage. Steam machinery, catapult piping, arrestors, carrier ops, all gone. Machine shops? Cut those back and re-purpose them to ship maintenance. That will free up a lot of space and mass.

Third bit, food and water. Assuming that whatever plague can't be transmitted through consuming fish, the bulk of the ark's diet will be based on fish, seaweed, maybe using algae as a supplement, and hydroponically or aeroponically grown citrus. A meat based diet like those of the Inuit actually provides all the nutrients and vitamins you need as long as the whole animal is consumed - but fruits and vegetable carry vitamin C in much larger quantities and are thus the best source for it. That means you can afford to feed a much larger population than you'd expect if you're assuming that you're growing everything on board.

Fourthly, corrosion and fouling. As others have mentioned, seawater is beastly stuff. But, there are ways around it. Sacrificial anodes have been mentioned, and it's simple enough to just stock up on a whole bunch of those. Wrap them up in airtight bags and attach them to floats then toss them overboard on a line if you've run out of space on board.
Fouling wise, you CAN remove it while still at sea, it's just more of a hassle than it's worth, which is why it's usually done in dock. But there's nothing stopping you from coming to a dead stop and sending out a bunch of divers with electric scrubbers to scrape off fouling. You can take it a step further if you have the equipment, and you can always set it a few years in the future and say they've got ultrasonic anti-fouling hull vibration systems or electrified graphene coatings.

Fifthly, weather. No great way around this. You'd want to keep north, where the water is too cool for hurricanes to form. Not south, because the waves there get really high. Still, you'd need some power to station-keep. By the time your nuclear reactors spool down, the carriers should have working kite sails to be able to maintain some maneuver capability. Their size works for and against them: they're big and thus stable in high seas, but they're also difficult t move with wind alone.

Finally, is this infection magically bound to all pieces of land? There are a lot of uninhabited islands out there that would be a lot more viable for long term habitation than living on the ocean all the time.

Assuming dirt farming, as opposed to large scale industrial hydroponics, aeroponics, or mycoculture it takes roughly an acre of land to feed a human for a year. We can reduce that somewhat if we assume that the fleet harvests plankton, krill and other high density marine life. Further still if the fleet can take advantage of some of the more advanced techniques available to the modern close space farmer but you're still looking at relatively large volumes of space for farming per person.

I think the fleet is done for; let's look at an example: The flight deck of the Abraham Lincoln is roughly 6 acres and it ships nearly 5700 crew and flight wing.

The bigger problem is that none of the ships will be afloat after more than a couple of decades at most, seawater is one of the most corrosive substances known to man, without regular changes of their sacrificial anodes ships hulls will simply fall apart. Without anti-fouling measures, that require dry dock time to complete or renew shear weight of marine life will sink ships.

Your generation ships will have 99 problems. Food and fuel won't be two of them.

Food won't be a problem if you like fish.

Fuel is a bit trickier, and requires command staff to know at the outset that their nuclear carrier is now a generation ship. Let's pause to look at the nuclear ship refueling cycle.

The refueling cycle

When a reactor shuts down, nuclear fuel keeps making heat. Civil reactors handle their fuel "wet". CanDU and RBMK have removable plugs that allow machines to swap fuel rods while the reactor is underway, and it's kept wet in the machine. BWR/PWR/VVER types, you have to shut down and pop the lid off, and the spaces above the reactor lid are a huge pool that you flood. (e.g. the worrisome fuel pool in Fukushima reactor 4). That's how you manage decay heat.

With military reactors, there's no space for that. So you must wait a long time for the fuel to cool enough to even start your refueling operation, so you use that time to do a systems overhaul as well. This whole deal takes 3 years.

So. Suppose your ship is on year 25 and the drydock is ready. But wait! War is imminent in the next 1-3 year; you'd be caught in drydock. That won't do. So your refueling/overhaul is deferred. In year 27 war begins, you see robust action through year 32, but no overhaul yet: another boat needs it more due to battle damage. So year 35.

Also, suppose on year 35 they have been idling for 12 hours and suddenly they gotta go Right Now. That reactor will in a Xenon Pit. So it'll be built with the control-rod "authority" to quickly blow through it and regain full power, without resorting to safety violations like Chornobyl. We're talking a lot of reactivity and rod authority that will keep it going when it doesn't have a xenon pit.

Military reactors are sized for contingencies.

Getting to 150 years

Nuclear fuel is pretty simple: fuel burnup is proportional to the heat energy you use. Carrier reactors are sized for a career of high tempo maneuvering: lots of fast cruise and generous use of energy since it's plentiful.

If you can reduce power consumption, your reactor lasts longer in proportion. Making it to 150 years takes about an 80% cut in energy usage. Obviously you will be quitting flight ops, and minimizing sea cruise. Keeping propulsion at tickover, just enough to maintain sea stability, or weighing anchor somewhere, will be key. Then you cut down your electrical loads and reduce your heating loads with good insulation (which you didn't really need before).

I would expect that most of the time, one of the two reactors would be shut down. The ship is more than capable of fighting on one reactor, so it should be able to serve in "generation ship" mode with one reactor at low power.

The experience of the civil nuclear industry is that reactors age quite well. There haven't been an appreciable number of new US plants since the 1980s, so they're all quite old - and yet they are repeatedly recertified, even in a post Chornobyl post Fukushima age. The only major difference is that carrier reactors use salt water as an ultimate heat sink in heat exchangers, and corrosive salt water may be an issue.

One option to slow or arrest salt water corrosion is for the carrier group to relocate to a river which allows them to sail sufficiently upstream to be in fresh water. As discussed, this would be one of their 99 other problems.

One way to deal with hull maintenance is to use bulldozers, tides and pumps to make a man-made basin, and an improvised "lock" made by pushing dirt around. Float the carrier into the "lock", fill the lock and basin, float the carrier into the basin, then open the "locks" and let the carrier settle onto the earth - the equivalent of blocks in a drydock. Then, to reach the carrier bottom, you tunnel the dirt out from under the carrier, in narrow strips of maybe 20 feet wide, so 90% of the carrier bottom is still supported by earth. You remove barnacles and replace the bottom antifouling, and when it cures, refill that tunnel and dig another tunnel. You could do this in a continuous "bubble", digging out on the aft side of the tunnel and repacking the dirt in the forward side. When the process is done, have the bulldozers re-create the "lock", pump the basin full of water, and float the carrier back to sea.

FOOD

As others have mentioned, food isn't an issue. You have fish and you have seaweed. You can farm fish and also do things like grow oysters on strings. Some vertical farms on the boats could grow some land vegetables (with compost adding to the soil so it doesn't deplete). Fermenting the vegetables in brine (easy to come by) gives you plenty of Vitamin C, probiotics, and B vitamins.

Once the colony is formed, the fish and sea vegetables will need to come from smaller crafts sent out for gathering. Why? Because of the human waste generated by the colony that goes into the surrounding ocean. Yes it helps feed plants and animals but it's not sanitary to harvest directly from it.

WATER

Fresh water is a much bigger problem. Mostly this is for drinking/cooking. While humans feel better bathing in fresh water, it's not required. When there is heavy rainfall, the excess fresh water can be used for laundry and cleaning to get salt residue off.

Rain is uneven and you need enough fresh water storage containers to carry you through to the next heavy rainfall. Dew and condensation collectors can help bridge the gap. And there could possibly even be desalinization technology that works on the right scale to make a difference.

The main issue here though is time. Not just the time between rainfalls, but time ruining your equipment and damaging your storage containers. Plastic containers won't last 150 years (they probably won't last 20 years, especially if exposed to the sun). Metal containers will corrode and develop leaks. They can be repaired, but eventually the patches aren't going to do the trick.

Collectors also will develop holes and leaks. Something as simple as a hanging tarp to allow dew to form overnight and drip into a bucket will not work in a few years because the materials have degraded so much (and can't be replaced). Desalinization equipment will also break down.

CANNIBALISM

Cannibalism can take two forms:

1. Deliberate "culling" of people for food.


2. Making use of the bodies of people who have died.

Either way though, it doesn't make much sense. There's no need to eat human flesh because there will be plenty of fish in the sea, even after 150 years of local eating.

Population control is a big issue though and there won't be any birth control available after the first few years, aside from periodic abstinence (which works better than people think but only if you care, chart, and don't cheat). That's not cannibalism but it may give your story the right amount of horror you want.

There is also the issue of criminal behavior. There could be some prison space (perhaps even a prison boat) but it's not practical to punish people by locking them up long-term. For people where "community service" and plain old shunning/shaming doesn't work, there might be a death penalty.

If you really want some cannibalistic element, use prisoners' bodies to feed the fish farms.

POPULATION

The number of people you can have will depends obviously on the capacity of each ship plus how many ships you have. Some ships might need to be workstations or for storage. If not, then you need to allocate space for those things within ships. Ditto for food and water storage, food processing, and general storage.

Food supplies won't limit the population (it does on Earth now but your ships will only have a fraction of what Earth has). But water supplies will, especially as your storage capacities diminish over time.

The aircraft carrier will not last that long.

A standard cruise is maybe 2 years at a time before needing maintenance downtime in the yard. But during those 2 years there will be numerous resupplies, either at dock or using an auxiliary resupply ship in a maneuver called "UNREP" (Underway Replenishment). That supply ship is not a small boat.

20-25 years before the reactors need to be refueled. Planned service life 50 years with all the planned maintenance periods in dry dock. Maximum? Probably 65-70 but it would be in horrible shape by then.

Ships that old stuff like toilets, air conditioning, etc start breaking down. There are WWII ships that old still intact as museums but aren’t operational or seaworthy in any sense. The older the boat, the more expensive and difficult it is to maintain. This is not a good plan, it’s just too much work to keep aircraft carriers working.

Many of the answerers have done a good job pointing out the deficiencies in trying to keep a group of nuclear carriers afloat and functional for many years. However, I think we are giving short shrift to the problems of food, waste management, and public health. The crews of modern warships are generally extremely healthy young individuals, and every effort is made to maintain "herd health."

This will go out the window in a crisis situation with a non-military refugee population. Especially since the medical supplies will eventually run out and it's extremely unlikely any of the ships in the group will have any capacity for making more.

Completely apart from the terrible virus they think they are escaping, if they stay in those close quarters for long, disease will eventually become rampant and wipe them out.

Additionally, warships aren't designed to recycle their waste. They just hold it until they can conveniently get rid of it. Establishing some kind of reasonable waste recycling may be difficult or impossible in a refugee situation.

And even though several posters have claimed that food won't be a problem, a fish-only, protein-only diet will be... less than optimal for everyone's health over the years. The populace will need vegetables, and that requires at least an acre per person. More, to support the possibility of an increasing population and as a hedge against some crops failing.

The right solution is to stay at sea only long enough to find a reasonably isolated and "clean" location on land for most of the refugee group. That alone will be a huge task in such a setting, especially since most of the rest of the populace ashore may be assumed to be quickly dying off and unable to report on conditions. Time would be of the essence, and this would likely be a time (and resource) consuming task! Perhaps this could be the crux of the story?

Could some number of people survive without resorting to cannibalism? I think the answer is most certainly. Could 7 Billion people survive off harvesting the Pacific Ocean for 150 years? On average humans need 100 grams per day and 1500 calories. That's 700,000 kg per day of protein and a lot of calories. Today, we harvest 90 Billion kg of fish, muscles, and so on from all the seas around the world. So there seems like there would be enough food for a lot of humans. Survivability would be enhanced by colonizing the other oceans too, and not just the Pacific.

I think the biggest challenge would be power generation. They'll need to smelt metal to repair parts of their ships -- 150 years at sea is a long time, and ships rust.

Assuming no issues with the ships ventilation as stated by JBH, here are some solutions.

If your goal is to ensure the survival of humanity

Just do Adam and Eve for each ship. If each ship have a plot of land and fish, a pair (a male and female), they continue the human race; especially if there are multiple ships out in sea. Ideally, you would want a doctor or medical expert to be either the husband or wife and some specific vitamins to make up for the missing resources provided by eating meat.

Since there's only two human per ship, you can even bring in livestock like cows and chicken as they produce useful food items. Heck, if each ship brings a different combination of livestock and/or plants, they can implement a trading system where each ship (or family) can trade with other ships for essentials. This will ensure that each ship is specialized in one produce.

As for who gets to live and who gets to die, well, that's where this gets a bit nasty; it is the survival of the fittest. Those who are the healthiest and have useful skills (i.e. doctor, farmer, fisher) gets to live. While pairing should be compatible/lover, with the end of humanity, lovers can't be choosers.

Save as much people as possible

There are multiple suggestions of fishing/farming, but here is another, very disgusting, albeit doable way.

This is pretty bad, you have been warned

Eating one own poop could help offset some food issues provided that medications are abundant. This is because the digestive system cannot 100% process what we eat fully and thus our waste still have some benefits.
There are health risk with this obviously, but that is where medication comes into play. Meds are generally small and last a long time.
The idea is for the rest of the years, carefully balance fishing/farming and eating poop to survive. And every other or so excretion gets reused as food (obvious for oneself, it is already bad as it is, but force other to eat yours?).

The main idea is not to exhaust the sea and whatever land you have. Over fishing and and planting can greatly tax the resources and led to early depletion of resources. So by limiting the amount of fishing and farming via other means, one can last longer. Also, the waste can be used as fertilizer to help rejuvenate the land and with careful amount, attract micro-organisms which can then attract big predators, leading to more fishes.

The reason I did not mention bring livestock in this case is that humans + livestock = too much waste and thus cause heavy pollution which can easily led to quicker contamination of water and air. Especially cows.

Screw the World

This one is pretty much ignore the disease and move back to land. Humans are very adaptable creatures and a group of people may be able to become immune to the disease.

To help with this crazy idea, lets go even crazier. Radiate people; you got nuclear reaction at your fingertip. Mutation can lead to genes which could help the person survive the disease. What kind and how much? That is up for grab and chance.

Would not recommend if you want to see humanity live; would be a fun simulation tho.

Cannibalism just doesn't work in that setting. It can be a solution for relatively short periods of times. Maybe for a year or two (stranded in north pole or surrounded by enemy soldiers for less than a year) but eating people will cause serious issues. First of all is the amount of human meat in a body. Assuming things are not going well the average weight of average person on that ship has gone down to 65kg on average. Men and women alike lost their body fat and become more more fragile, skinny and tired. And people won't start eating other people until they have done and waited as long as possible. This means that average body has less stuff to eat. According to some googling about 80% of human body weight is edible. So one body is about 52kg of food. And one kilogram of human meat might have 1500 calories.

Using gerald r ford aircraft carrier as an example that holds a crew of 2600. So let's assume we triple that mount and remove all the airplanes and weapons to make it still float. That is 7800 people. Pure guess. Let's say 700 calories per day is minimum to survive. This is awfully low amount as you'd need to be able to work hard to keep fixing the ship as all its systems are massively overloaded due to tripling of the number of people onboard. But you have kids onboard as well who eat less.

So from those numbers we can quickly conclude that relying on cannibalism alone won't work. Daily for that amount of people you'd need 5200kg of human meat! You'd need to be killing 56 people PER DAY just to survive. It just doesn't work at all. If you want a math challenge you can work out how long until all but one person is dead from that 7800 people. One person needs 700 calories per day, meat has 1500calories per kilogram, one person weighs 65kg.

And if that is not enough you'll create massive problems with who gets to live and who gets eaten. You are asking people to commit mass scale murder on daily basis. People having to eat their spouses, kids, mothers and fathers. Not to mention the effort it takes to prepare all that food. Killing, cutting it up, cooking it... You don't want to eat raw meat as it has less calories than cooked meat. So you need a lot of electricity or wood to heat up the meat as well. Plus all kinds of other issues. When the food runs out cannibalism won't save you. It might help handful of people out of big group to live a year or two longer at most.