Additional invariants and statistical equilibria for the 2D euler equations on a spherical domain
Herbert, C. (2013). Additional invariants and statistical equilibria for the 2D euler equations on a spherical domain. Journal Of Statistical Physics, 152, 1084-1114. doi:10.1007/s10955-013-0809-6
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 int... Show moreThe 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. Show less
