  The theoretical study of the self-organization of two-dimensional and
geophysical turbulent flows is addressed based on statistical mechanics
methods. This review is a self-contained presentation of classical and recent
works on this subject; from the statistical mechanics basis of the theory up to
applications to Jupiter's troposphere and ocean vortices and jets. Emphasize
has been placed on examples with available analytical treatment in order to
favor better understanding of the physics and dynamics. The equilibrium
microcanonical measure is built from the Liouville theorem. On this theoretical
basis, we predict the output of the long time evolution of complex turbulent
flows as statistical equilibria. This is applied to make quantitative models of
two-dimensional turbulence, the Great Red Spot and other Jovian vortices, ocean
jets like the Gulf-Stream, and ocean vortices. We also present recent results
for non-equilibrium situations, for the studies of either the relaxation
towards equilibrium or non-equilibrium steady states.
