For inertial oscillations, see Durran (1993, Journal of the Atmospheric Sciences); for detailed discussions of inertial circles and inertial oscillations see classical texts (Gill, "Atmosphere–Ocean Dynamics"; Pedlosky, "Geophysical Fluid Dynamics"; Vallis, the course textbook). The modified vertical inertia problem is a common exercise illustrating hydrostatic vs nonhydrostatic behavior.
