HAMILTONS PRINCIPLE FOR QUASI-GEOSTROPHIC MOTION

We show that the equation of quasigeostrophic (QG) potential vorticity conservation in geophysical fluid dynamics follows from Hamilton's pr inciple for stationary variations of an action for geodesic motion in the f-plane case or its prolongation in the beta-plane case. This impl ies a new momentum equation and an associated Kelvin circulation theor em for QG motion. We treat the barotropic and two-layer baroclinic cas es, as well as the continuously stratified case. (C) 1998 American Ins titute of Physics.