91福利

The equilibrium statistical mechanics of two dimensional and geostrophic turbulence predicts the outcome for the large scales of the flow, resulting from the turbulent mixing. I will focus on physical ideas in order to emphasize how concepts from statistical ideas: phase transitions, phase diagrams, and phase coexistence, have been successfully applied to geophysical fluid dynamics. For instance this theory allowed us to model the detailed properties of the Great Red Spot and other localized structures of Jupiter's troposphere.

A first aim of the talk is to discuss the range of applicability of this theory to ocean dynamics. This range is probably limited due to the inertial assumption underlying this equilibrium approach. Still we will show that the theory is able to reproduce in detail localized structures like westward mid-basin jets (Gulf Stream, Kuroshio) and ocean vortices (rings). We also uncover the relations between strong eastward mid-basin inertial jets, like the Kuroshio extension and the Gulf Stream, and statistical equilibria. An important (and justified) criticism of the equilibrium theory is its inability to take into account the forcing and dissipation, which play an essential role. The second aim of this talk is to present new results for a non-equilibrium theory of the mixing of the potential vorticity that takes these into account. We first describe new sets of invariant measure. We show that we can predict from these non-equilibrium phase transitions, where the flow switches randomly between two different large scale patterns. The main interest of the theory is to predict the range of parameters of this bistability phenomenon and to predict the mean streamfunction for each of these two states. We discuss future geophysical applications of these new theoretical results.