Seminar- Large-scale atmospheric flows predicted by statistical mechanics

Two-dimensional turbulent flows are known to develop large-scale coherent structures which can be explained and predicted by statistical mechanics in a relatively satisfactory way. Given a small set of macroscopic quantities (energy, circulation, enstrophy...); it is possible to compute the equilibrium state ultimately reached by the flow. Phase diagrams classifying the different flow structures obtained for the different values of the macroscopic parameters can be constructed. Applying this theory to a simple model of the atmosphere (the quasi-geotrophic equations on a rotating sphere), I shall show that in the absence of a bottom topography, the statistical equilibrium states are only purely zonal, solid-body rotations, and symmetry-breaking dipolar flows. In this case, the phase diagram displays a second-order phase transitions between these two equilibria for a critical value of the energy. When a bottom topography is added, we obtain other possibilities reminiscent of the atmosphere of the Earth. Although these new states are formally unstable in the statistical mechanics framework, they may be long-lived in practice and thus relevant for atmospheric modelling. I will also discuss the puzzling thermodynamic properties of the statistical equilibria (negative statistical temperatures, vanishing specific heat, non-concave microcanonical entropy...) in relation with the general problem of statistical mechanics of systems with long-range interaction.