Thought experiment regarding a posible preferential configuration of tectonic plates Oceanic and continental tectonic plates have different densities, and their relative position have a very important effect on the evolution of Earth's climate on geologic time scales. There are many factors that control the position of tectonic plates, but I'm wondering if there is any forcing arising from the density difference in a rotating planet.
Please consider the following thought experiment:
Imaging a rotating volume of water with the mass of the Earth, and rotating as Earth's does (pretty much with equal angular speed at all depths), but in thermal equilibrium (i.e. no currents). Then, we cover the surface of the water with many floating spheres of equal size but with two different densities. The two kinds are distributed randomly at the start.
Now:
Would the heavier spheres migrate to the equator? Would they migrate to the poles? Or there is no segregation mechanism and there will remain in a random distribution?
 A: Segregation usually comes about because that configuration represents a lower energy configuration than some other.  In a vertical column, having higher density elements at the bottom is a lower energy state than having higher density items at the top.
For the rotating mass of water, the surface will in the long term deform to form an equipotential surface.  As such, having the objects in different surface configurations does not represent any change in energy.  There's no reason to prefer one configuration over another from an energy standpoint.
Another way to think about this is that we can imagine a "chunk" of water to be much denser than a "chunk" of air.  If we drop one of these chunks anywhere on the world, where would it go?  The answer is that if it would be favorable to migrate to the equator, other chunks of water would have already done so.  The water piles up at the equator to precisely the height that compensates for the rotational acceleration.  Since the water has already moved so that there's more of it at the equator (and it's now farther from the earth's gravity pull), there's no longer any driving force for floating objects to preferentially move there as well.
