Analogies of ocean/atmosphere rotating fluid dynamics with gyroscopes: Teaching opportunities

A simple tangible device that has analogous dynamics to the rotating shallow water (RSW) system, the gyroscope, or spinning top, is studied. Rotating rapidly, the gyroscope seems to defy gravity by not falling over, as long as it possesses sufficient spin. Building intuition about geostrophic flow and inertia-gravity waves in the RSW system is important, however, because it provides a solid foundation for understanding more complex motions in real environmental fluids. Geostrophic flow occurs when the nondimensional Rossby number is small. When centripetal and Coriolis forces are similar in magnitude, the Rossby number is near one (called gradient wind balance). Even closer to the cyclone center, the centripetal force dominates the Coriolis force and the Rossby number is large. Geostrophic flow and inertial oscillations are also easily shown using a rotating laboratory turntable. Clear and distinct differences exist between the gyroscope and the longwave limit of the RSW system because of the different geometrical prefactor in the Coriolis term.