Statistical ensemble inequivalence and bicritical points for two-dimensional flows and geophysical flows

A theoretical description for the equilibrium states of a large class of models of two-dimensional and geophysical flows is presented. A statistical ensemble equivalence is found to exist generically in these models, related to the occurrence of peculiar phase transitions in the flow topology. The first example of a bicritical point (a bifurcation from a first toward two second order phase transitions) in the context of systems with long-range interactions is reported. Academic ocean models, the Fofonoff flows, are studied in the perspective of these results.