The two-dimensionality of slow motion in a rotating fluid

The Proudman-Taylor theorem states that, in a fluid rotating steadily about a vertical axis, if a flow pattern is induced—for example by the slow steady motion of a solid body such as a squat cylinder at one level—the same flow pattern is induced at all levels by Coriolis forces. The steady equilibrium situation is simply understood in terms of a balance of the horizontal Coriolis forces at all levels. The mechanism providing the accelerations whereby the equilibrium is established is shown in various examples to involve vertical transport of momentum by flow around loops linking the various levels. The limited role of this mechanism in atmospheric circulation, in the dynamo action in the earth's fluid core responsible for terrestrial magnetism, and in the liquid-drop model of nuclear rotation is briefly discussed.