Phase transitions and marginal ensemble equivalence for freely evolving flows on a rotating sphere

Corentin Herbert (1, 2) , Bérengère Dubrulle (1) , Pierre-Henri Chavanis (3) , Didier Paillard (2)

1 SPEC - UMR3680 - Service de physique de l'état condensé
2 LSCE - Laboratoire des Sciences du Climat et de l'Environnement [Gif-sur-Yvette]
3 PhyStat - Physique Statistique des Systèmes Complexes (LPT)

The large-scale circulation of planetary atmospheres like that of the Earth is traditionally thought of in a dynamical framework. Here, we apply the statistical mechanics theory of turbulent flows to a simplified model of the global atmosphere, the quasi-geostrophic model, leading to non-trivial equilibria. Depending on a few global parameters, the structure of the flow may be either a solid-body rotation (zonal flow) or a dipole. A second order phase transition occurs between these two phases, with associated spontaneous symmetry-breaking in the dipole phase. This model allows us to go beyond the general theory of marginal ensemble equivalence through the notion of Goldstone modes.

Domaines: Mécanique statistique [cond-mat.stat-mech]; Dynamique des Fluides [physics.flu-dyn]; Physique Atmosphérique et Océanique [physics.ao-ph]

Corentin Herbert, Bérengère Dubrulle, Pierre-Henri Chavanis, Didier Paillard. Phase transitions and marginal ensemble equivalence for freely evolving flows on a rotating sphere. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2012, 85 (5), pp.056304. ⟨10.1103/PhysRevE.85.056304⟩. ⟨cea-00917336⟩