It boils down to the changed shape of the *displaced water* under rotation of the hull. Ideally, any rotation about the COG should *dramatically increase* the displacement, thus raising the COG enough to supply a force counter to that twisting the hull in the first place. For example, a fast sailing ship leans over & increases its displacement, until the force trying to right the ship equals the force of the wind. Fast sailing yachts take advantage of this principle to dramatically *increase the length of the waterline* because the longer hulls can go faster for the same total displacement. At 10:30 PM 7/29/2018, Jason Holt wrote:

I just learned about free surface effect: https://en.m.wikipedia.org/wiki/Free_surface_effect

And it makes me wonder: imagine a cross section blueprint of a ship perpendicular to the keel. We want to design the cross section of an oil compartment that will run stem to stern and minimizes free surface effect.

To keep it simple, let's just consider a static case where the ship has listed to port or starboard and the fluid in our tank has settled. The tank is, say, 50% full. Can tank shape affect the ship's change in center of gravity?