Effect of water on wobble of rotating structure If we have a structure that rotates to create artificial gravity, then if the mass isn't perfectly distributed along the circumference the CM will be offset from the geometric center so there will be a wobble.
I made this illustration, to show the wobbles that happens becuse a person goes to visit his/her friend on the opposite side of the structure.

Some artist conceptions include water in the forms of lakes, and are often contiguous bodies of water that circle the entire circumference (Bernal sphere example).  If we assume there is a free-flowing body of water around the entire circumference like this (and is sufficiently deep), then it's clear that water will move as a result of a mass movement since the previous water surface is no longer equipotential.  This will also move the CM.
How would the presence of water affect the wobble?
 A: The system CM is the only thing we can identify that is truly inertial.  Make that the origin.
It should also be noted that the CM is a combination of the mass-weighted CM of all the components.  Those components are:


*

*The man that moves

*The rigid structure

*The body of the water, which I will break down into geometric parts:


*

*The outer edge, or the "lake floor"

*The surface, which is always a circle about the system CM



The last point is absolutely crucial, but let's sum up the entire course of events.
The man moves in the negative y-axis direction (down).
Since the system CM remains in place, the CM of the (structure + water) moves in the positive y-axis direction (up).
We can guess that the rigid structure moves "up" as in the OP illustration.
As we imagine that, the lake floor moves but the surface doesn't.
That means the lake's mass moves "up" - the same direction as the structure.
From this information alone we conclude that the wobble is lessened by the presence of the water.
Let's go deeper into the dynamics of the water.
The water is an annular region.  As the rigid structure moves up, the outer edge moves up, making the annulus into a shape like a crescent moon.

When the structure moves, it moves the outer circle but
the inner circle remains in the exact same place relative to the CM of the system.
So the inner circle can't factor into the calculation for the revised location of the water's CM.
The center of mass of the water, is thus weighted as if the inner circle just isn't there.
That will create an extremely large "artificial" mass of the water that will decrease the wobble of the system.
The water decreases the amount of wobble as much as you would get if the entire thing was fully filled with water!
To the extent that you're not drying out any part of it this will be true, and it will be irrelevant of the level of the water.
A: Ce n'est pas une réponse.  (Where are the hydrodynamicists?)
Have you considered the possibility of "tsunamis"?
Gravity waves have an approximate wave velocity $v_w = \sqrt{gh}$, with $h$ the water depth and $g=v_s^2/R$ the radial acceleration (of a cylindrical shell with radius $R$ and wall velocity $v_s$).  
So $v_w = \left(\sqrt{h/R}\right) v_s $, and the wave velocity is less than the shell's.  
The question is whether a particular standing wave pattern could become resonant and extract energy from the rotating shell to increase the wave's (and the wobble's) amplitude. 
I have no idea how to figure that out.  
