Physics – Fluid Dynamics
Scientific paper
2009-04-14
Physica D, 237, 1998 (2008)
Physics
Fluid Dynamics
Proceedings of the international conference "Euler Equations: 250 Years" (Aussois, France 18-23 June 2007). Edited by G. Eyink
Scientific paper
10.1016/j.physd.2008.02.027
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.
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