Equilibrium Statistical Mechanics of Barotropic Quasi-Geostrophic Equations

Abstract

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.

18 pages

Cited by in corpus (3)

• Dissipation properties of transport noise in the two-layer quasi-geostrophic model
• Gibbs Equilibrium Fluctuations of Point Vortex Dynamics
• On the infinite dimension limit of invariant measures and solutions of Zeitlin's 2D Euler equations