Applications of equilibrium statistical mechanics to atmospheres and oceans

We discuss statistical mechanics models of ocean and atmosphere flows. This theoretical approach explains the self-organization of turbulent flows described by the quasi-geostrophic equations, and predicts the output of their long time evolution. On these short lectures, emphasize has been placed on examples with available analytical treatment in order to favor better understanding of the physics and dynamics. We obtain quantitative models of the Great Red Spot and other Jovian vortices, ocean jets like the Gulf-Stream, ocean vortices, and we make quantitative predictions of vertical energy transfers in the ocean. A detailed comparison between these statistical equilibria and real flow observations or numerical simulations is provided.