The official U.S. Navy Fleet Type Submarine manual contains basically the same info as the article the OP linked to.
To summarize, a surfaced submarine with dry tanks or a submerged submarine with flooded tanks is stable.
In between, a submarine with partially flooded tanks will reach a point where its "center of buoyancy" and "center of gravity" will coincide. At that point it is unstable and could potentially capsize. When a sub is diving or surfacing that point is passed quickly, so it is not a practical issue, but it could be dangerous in a "Decks Awash" situation:
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At A, the vessel is floating with all water excluded from the tank surrounding the chamber. The center of gravity is at G and the center of buoyancy, B, is found by intersecting diagonals of the displacement.
At B, water has been admitted to the lower section of the tank. Using the diagonals as before, it is seen that the center of buoyancy, B, is now coincident with G and the unit is unstable.
At C, the surrounding tank is flooded and the unit is submerged. The center of buoyancy is at B2, the intersection of the diagonals of the displaced water. The unit is stable, the center of buoyancy and the center of gravity are in the same vertical line. Any rotational movement about the center of buoyancy B2 immediately sets up a restoring moment arm
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full discussion here at pp. 55-61:
http://www.maritime.org/fleetsub/chap5.htm#5B
In addition, when you look at the operation of the tanks during a dive, you can see the difficulty in maintaining a stable "Decks Awash" situation:
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The weight taken on is water, and it is flooded into tanks. The air, of course, is vented off the tanks as the water flows in. First, the large tanks, known as main ballast tanks, are flooded. These tanks hold 359 tons of sea water. (See Section 4A2.) The submarine now displaces 2,109 tons and draws approximately 22 feet of water. The main deck is not awash, since there are approximately 2 feet from waterline to deck. The ship still has plenty of positive buoyancy. Since the bow buoyancy tank vent has been open during this operation, allowing this free-flooding tank to take on ballast as the ship submerges, it is necessary to add to the displacement the weight of water taken on by the bow buoyancy tank (which belongs to the special ballast tank group).
This gives a new total displacement of 2,141 tons (2,109 tons plus 32 tons).
Simultaneously with the flooding of bow buoyancy, the safety tank also in the special ballast tank group, is flooded. This tank holds 23 tons of water, giving a total displacement of 2,173 tons and a draft of 24 feet. The decks are just awash, and some positive buoyancy is still retained, although the submarine is approaching a condition of neutral buoyancy. Two things remain yet to be done: 1) to take on additional weight, and 2) to distribute this weight so that fore-and-aft athwartship balance is maintained. This additional weight is added to the variable ballast tanks and distributed throughout the variable tanks by the trim system. With the ship in this condition, approximately 55 tons of water must be added to the variable tanks to submerge to a depth where the periscope shears are even with the waterline. The ship is not in a state of neutral buoyancy and is balanced both fore-and-aft and athwartship. At this point, any additional ballast taken on will cause the submarine to submerge; any ballast removed will cause it to rise (Figure 4-1).
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http://www.maritime.org/fleetsub/chap4.htm#4B
To summarize, to get the sub to a "Decks Awash" state in a dive, the main ballast tanks, bow buoyancy tank and safety tanks are flooded. However, the bow buoyancy tank is located in the bow and causes the sub to become nose heavy to make a dive easier. To maintain level "Decks Awash", the bow tank would have to remain dry and certain other of the variable ballast tanks flooded so that the sub is balanced both along its fore and aft and side to side axis. It is certainly theoretically possible, but would appear difficult to do in anything other than calm waters.
Again, I suspect that when a skipper wanted to lower the sub's silhouette, he would just flood the main ballast tanks which would bring the deck down from 10 feet to 2+ feet above the waterline. In the open ocean, that would usually result in waves breaking over the deck so the decks are "awash".
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Originally Posted by troopie
@Bilge Rat: love your Avitar mate! Staunch, grumpy, alcoholic; I should have Captain Haddock as my Av. 
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It seemed the right persona for THIS forum....
