  We consider equations describing a barotropic inviscid flow in a channel with
topography effects and beta-plane approximation of Coriolis force, in which a
large-scale mean flow interacts with smaller scales. Gibbsian measures
associated to the first integrals energy and enstrophy are Gaussian measures
supported by distributional spaces. We define a suitable weak formulation for
barotropic equations, and prove existence of a stationary solution preserving
Gibbsian measures, thus providing a rigorous infinite-dimensional framework for
the equilibrium statistical mechanics of the model.
