Statistical mechanics of 2D turbulence with a prior vorticity distribution
Abstract
We adapt the formalism of the statistical theory of 2D turbulence in the case where the Casimir constraints are replaced by the specification of a prior vorticity distribution. A phenomenological relaxation equation is obtained for the evolution of the coarse-grained vorticity. This equation monotonically increases a generalized entropic functional (determined by the prior) while conserving circulation and energy. It can be used as a thermodynamical parametrization of forced 2D turbulence, or as a numerical algorithm to construct (i) arbitrary statistical equilibrium states in the sense of Ellis-Haven-Turkington (ii) particular statistical equilibrium states in the sense of Miller-Robert-Sommeria (iii) arbitrary stationary solutions of the 2D Euler equation that are formally nonlinearly dynamically stable according to the Ellis-Haven-Turkington stability criterion refining the Arnold theorems.
Keywords
Cite
@article{arxiv.0904.2145,
title = {Statistical mechanics of 2D turbulence with a prior vorticity distribution},
author = {Pierre-Henri Chavanis},
journal= {arXiv preprint arXiv:0904.2145},
year = {2009}
}
Comments
Proceedings of the international conference "Euler Equations: 250 Years" (Aussois, France 18-23 June 2007). Edited by G. Eyink, U. Frisch, R. Moreau and A. Sobolevski