{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"710975a252c03ce9076302f8eac38901ee802bf838363b61216a232f900b3048","created":"2026-10-03T07:18:03Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"cdfab807543d9b321e1432a9e15fdc2651897e114b5e255eacb5171bd3ce063e","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"classification","assisted_by":[],"external_id":"fluid.2d-turbulence.statistical-equilibrium","kind":"phenomenon","literature_status":"open","n":"1","parents":[],"plain":"Freely decaying flat turbulence organizes itself into a few large vortices or jets, and a theory from statistical mechanics predicts the final pattern by maximizing a mixing entropy. The prediction works in some cases and fails in others, and no rule says when.","posed_since":"","precise":"For 2D Euler or high-Re Navier-Stokes flow from given initial vorticity in a bounded or periodic domain, the Miller-Robert-Sommeria theory predicts the late-time coarse-grained vorticity as the maximum-entropy state constrained by energy and by all integrals of functions of vorticity (Casimirs). Determine the conditions on initial vorticity distribution, domain geometry and Re under which the observed late-time state matches the prediction, and characterize the incomplete relaxation where it does not. Answer: a criterion validated by DNS and experiment.","problem_ref":null,"references":"","settled_by":"Ensembles of high-resolution DNS and soap-film or thin-layer experiments compared with computed equilibria, with a criterion that predicts agreement or failure in advance.","status_note":"Cases of agreement and of incomplete relaxation are reviewed in Bouchet and Venaille, Physics Reports 2012.","title":"When does decaying 2D turbulence reach its statistical-mechanics 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