### Taylor-Proudman theorem

(theorem regarding movement through a rotating fluid)

The Taylor-Proudman theorem says when a solid body is moved (at most) slowly within a fluid that is steadily rotating at a high angular velocity (relative to the solid body's motion, if any), that the fluid velocity is uniform along any line parallel to the axis of rotation. If the solid body is cylindrical (unvarying shape) through the height of the rotating fluid (presuming the fluid is rotating around a vertical axis), this result is intuitive, but if the body is "shorter" than the height of the rotating fluid, the fluid not only flows around the object but flows as if the object were the full height of the rotation, i.e., around a virtual object projecting it to all levels, a far less intuitive phenomenon. In the atmosphere of a rotating planet, this could be flow around an object at ground level affecting the flow above the object as if the object were taller. This vertical region of fluid-rotation is called a Taylor column. The phenomenon is explained through the mathematics of fluid dynamics, and is confirmed by fairly simple experiment. This theorem has been used in an argument that Jupiter's Red Spot must be shallow because if it were deep, it would project a complimentary red spot in the other hemisphere.

(fluid dynamics,rotation)