THE TIME-DEPENDENT BEHAVIOR OF A SPINNING DISC ON A ROTATING PLANET -A MODEL FOR GEOPHYSICAL VORTEX MOTION

A recent theory of Nycander (1996) establishing the analogy between th e steady westward drift of geophysical vortices and the precession of a rigid-body (in particular a disc spinning about its symmetry axis) i s rederived within a Lagrangian framework. This formulation allows the time-dependent properties (e.g., trajectory, spin etc.) of the rigid- body, represented by three coupled ODEs, to be studied. Numerical resu lts for a variety of initial zonal velocities and latitudes are presen ted. Typically the trajectory consists of a mean westward precession c oupled with periodic behaviour which, in the terminology of rigid-body dynamics, is known as nutation. In the limit that P-plane physics are appropriate, it is shown that the nutation is exactly analogous to ha rmonic inertial oscillations at the local Coriolis frequency.