Gyroscopic analog for collective motion of a stratified fluid (Q1096502)

A precise analogy is drawn between circulation of a stratified fluid in a gravitational field, and angular momentum of a gyroscope. Collective dynamical equations for a stratified fluid are derived from tensor spatial moments of the fluid motion equation in the Boussinesq approximation. From the collective dynamical equations the gyroscope equations arise as a special case. In two dimensions the gyroscope equations reduce to the pendulum equation, which describes planar convection as ``angular sloshing'' whereby the density gradient vector of the stratified fluid undergoes pendulum motion in a vertical plane.