To begin with, the ship is floating on an even keel at
waterline WL. Then the compartment is flooded to
waterline W1. Assuming that the water enters the
compartment instantaneously and that it is
instantaneously frozen solid, the effects of this frozen
body of water are the same as if a solid weight had been
added. The ship undergoes parallel sinkage and comes
to rest at a new waterline W1L1.
Now suppose that an outside force acts on the ship,
causing it to heel over at a small angle of list to a new
waterline W2L2. If at the same time the liquid is freed
from its frozen state, it will run toward the low side of
the compartment until the surface of the water in the
compartment is parallel to the existing waterline
W2L2. A wedge of liquid is thus shifted from one side
of the compartment to the other; as a result, the center
of gravity of the liquid is shifted from D to E. As the
center of gravity of the liquid is shifted outboard, an
additional inclining moment is created. This causes the
ship to list to a new waterline W3L3.
The additional list, in turn, causes a further shift of
the liquid in the compartment and a further shift of the
center of gravity of the liquid. As the center of gravity
of the liquid shifts to F, another inclining moment is
created and the ship lists even more. Eventually the
ship will come to rest with a waterline such as W4L4.
This will occur when the righting moment of the ship is
equal to the combined effects of (1) the original
inclining moment created by the outside force and (2)
the inclining moment created by the shift of liquid
within the compartment.