1307.5109 (Corentin Herbert)

Additional Invariants and Statistical Equilibria for the 2D Euler
Equations on a spherical domain    [PDF]

Corentin Herbert

The role of the domain geometry for the statistical mechanics of 2D Euler flows is investigated. It is shown that for a spherical domain, there exists invariant subspaces in phase space which yield additional angular momentum, energy and enstrophy invariants. The microcanonical measure taking into account these invariants is built and a mean-field, Robert-Sommeria-Miller theory is developed in the simple case of the energy-enstrophy measure. The variational problem is solved analytically and a partial energy condensation is obtained. The thermodynamic properties of the system are also discussed.

View original: http://arxiv.org/abs/1307.5109