One of the fun tidbits that gets bandied around in physics departments is that the Mississippi River actually flows away from the center of the Earth. Due to the Earth's oblateness, the source of the Mississippi is actually significantly closer to the Earth's center than the mouth is, and it's only because of the Earth's rotation (and the centrifugal force present in a reference frame rotating with the Earth) that the water in the Mississippi ends up in the Gulf of Mexico.
My questions are two:
Does this mean that the Mississippi would flow north if the rotation of the Earth stopped? I'm leery of just looking at the distance to the center of the Earth, since the oblateness of the Earth also causes a distortion of its gravity field (i.e., the equipotential surfaces are no longer perfect spheres), and this distortion would seem to be on the same order of magnitude as the small differences in elevation we're considering. In other words, if one uses the actual gravitational potential for a non-rotating oblate spheroid, is the Gulf of Mexico at a higher gravitational potential than Minnesota?
Are there any other rivers in the world for which this is true? Obviously these would need to be rivers that flow towards the equator with a very shallow gradient (elevations measured relative to "sea level", which would be one of the equipotentials measured above.)
EDIT: For clarity's sake, assume that the Earth would remain the same shape if it wasn't rotating. (In reality, hydrostatic forces would eventually pull a non-rotating Earth into sphericity, but for this question I'm interested in the difference between an oblate, rotating Earth and an oblate, non-rotating Earth.)