Gyroscopes and rotating fluids: A pedagogical discussion of analogous dynamics

The dynamics of the rotating shallow-water (RSW) system is often surprising to people at first. But understanding RSW dynamics is a pre-requisite to understanding the dynamics of geophysical fluids, such as the atmosphere and ocean. The gyroscope is a simple device whose dynamics is also surprising. It seems to defy gravity by not falling over, as long as it spins fast enough. The links between rotating, rigid bodies, like gyroscopes, and rotating fluids are rarely emphasized, but in fact they are direct and revealing, and the two systems are mathematically isomorphic. Precession is seen to be analogous to geostrophic flow and nutation to inertial oscillation. The geostrophic adjustment process in rotating fluids can be illustrated using a gyroscope that exhibits transient adjustment to steady precession from rest. The controlling role of the Rossby number on RSW dynamics is reflected in a corresponding non-dimensional number for the gyroscope. For these reasons, the gyroscope can illustrate RSW dynamics and help students develop intuition about large-scale atmospheric and oceanic flow.