Course info

Rotating frames of reference, vorticity equation, Ertel’s theorem, Rossby number, Ekman number, Taylor-Proudman theorem. Geostrophic and hydrostatic balance, thermal wind relation, pressure coordinates, f and beta-planes. Shallow water and reduced gravity models, conservation laws for energy and potential vorticity, flow over topography, inertia-gravity waves, equations for nearly geostrophic motion, Rossby waves, Kelvin waves. Linearised equations for a stratified, incompressible fluid, internal gravity waves, vertical modes. Planetary Geostrophy. Quasigeostrophic approximation: quasigeostrophic potential vorticity equation and Rossby wave solutions, vertical propagation and trapping. Barotropic and baroclinic instability, necessary conditions for instability of zonal flow, Eady model of baroclinic instability. Wave-mean flow interaction, transformed Eulerian mean, Eliassen-Palm flux, non-acceleration theorem. Ekman layers and upwelling. Sverdrup balance and ocean gyres, western intensification, simple models for the vertical structure of ocean circulation and meridional overturning circulation. Angular momentum and Held-Hou model of Hadley circulations. Applications to planetary atmospheres.