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Abstract: We adapt the formalism of the statistical theory of 2D turbulence in the casewhere the Casimir constraints are replaced by the specification of a priorvorticity distribution. A phenomenological relaxation equation is obtained forthe evolution of the coarse-grained vorticity. This equation monotonicallyincreases a generalized entropic functional determined by the prior whileconserving circulation and energy. It can be used as a thermodynamicalparametrization of forced 2D turbulence, or as a numerical algorithm toconstruct i arbitrary statistical equilibrium states in the sense ofEllis-Haven-Turkington ii particular statistical equilibrium states in thesense of Miller-Robert-Sommeria iii arbitrary stationary solutions of the 2DEuler equation that are formally nonlinearly dynamically stable according tothe Ellis-Haven-Turkington stability criterion refining the Arnold theorems.



Autor: Pierre-Henri Chavanis

Fuente: https://arxiv.org/







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