What stops giant cruise ships toppling over in rough seas? A week ago, 2 of the most gigantic cruise ships in the world docked near my city. If you have seen one, or been on one, you will know how large they are.

They look extremely unsafe to me, although obviously safety features must be built into them to stop them listing so far over that they seem to me to be in  danger of toppling completely in rough seas or strong sidewinds.
I want to avoid the engineering side and to stick to the physics, which is simply based around the control of the angular momentum of the large vessels.
So my assumptions first, then my question.
I have searched Google for schematics of the design, but nothing jumped out at me, except a greater than expected list of people asking much the same question as this one. Are Cruise Ships Too Top Heavy? and Why Mega Cruise Ships Are Unsafe
They have shallow, but wide, bottom surfaces.  Either they have small keel surfaces, or they are able to pull the keel inside the ship, because the draught in my city port is fairly shallow and yet they were able to get well inside the harbor.
I guess they carry a large amount of ballast, they certainly have the room for it.
I also guess that the top floors are made of light material, so as to lower the centre of gravity as much as possible.
They almost certainly have stabilisers, that act to reduce listing and basically do the job that a keel does for sailboats.
My question is, does anybody with experience in fluid dynamics or related areas know 
what keeps these giant ships stable in roll and reduces their potential to list to large angles in bad weather?
EDIT I am hoping for a physics based answer, but I realise it may be a question for another site, I will migrate no problem  if need be END EDIT
 A: Some dimensions I was able to dig up (mostly from Wikipedia).
Draft of the Allure of the Seas: 31 ft (10 m)
Length: 1181 ft (360 m)
Beam at waterline: 47 m
Height: 72 m above waterline
Let's just draw the section based on these simple numbers:

Now if the center of gravity were in the middle of the ship (31 m above the water line), it would indeed not be very stable - any tilt beyond 25° would cause it to tip over:

However, there are several important factors:


*

*The part of the hull below the surface is made of much thicker, stronger, heavier material than the superstructure

*The engines etc. are all in the lowest levels

*There is an active ballast system that allows pumping fuel and sea water from side to side to help maintain balance


I found one online test of the stability of the hull of this ship in a test facility, where they made a big hole in the side of an accurate model to see how it would fare: https://www.youtube.com/watch?v=Ra4TkHOs4RE . While there are commercial interests at stake, nobody wants a marine disaster on their hands.
A: I doubt it is all fluid dynamics.  The have to stay upright even with dead engines.  If the integral of the lever below the water line is bigger than above then it should stay upright.  Ballast at the bottom goes a long way as it has a long lever.  Stuff like engines below deck tends to be heavy anyway.  Weight is not a big deal as they are not going up hill.  They need a low draft to get into port.  If you looked at an aircraft carrier out of water it would also appear top heavy.
Let assume a ship with 2/3 above water line.  Break the up in 9 units.  6 above and 3 below.
Naturally lightest stuff on top and heavy below. 
In this example the net lever above is 45 and below 180.    
Height Weight Lever 
6      1       6
5      2      10
4      3      12
3      4      12
2      5      10
1      5       6
net           56
1      10     20
2      20     40
3      40    120
net          180

Imagine that is a teeter-totter with 3 fat kids on one side and 6 skinny on the other.  Even if the skinny kids have twice the lever the fat kids still dominate.
Since it pivots on the hull and not the center line the bottom loses leverage as it starts to list.  So a narrow hull at the water line is a good thing.
A: As I understand it many seagoing vessels also use gyroscopes spinning on a vertical axis attached to the main components of the vessel's structure to null out much of the motion on the vessel's roll axis. Gyroscopes are also popular among motor yachts. I'm not Shure if they're used on giant cruise ships or not but, gyros are one way of providing stability, and safety.
A: a large lever attached with a ship will give a huge effort on other side that it can heat the water by driving an engine made of dc motor and emf give to heating element which operate on dc voltage  so it may work on either side to produce steam engine can produce electricity at a constant speed to provide for grid operation.
