Onsager's ensemble for point vortices with random circulations on the sphere
type: Item
instance of: scholarly article
title: Onsager's ensemble for point vortices with random circulations on the sphere
zbMATH Open document ID: 1263.82055
author: Yu Wang
author: Michael K.-H. Kiessling
published in: Journal of Statistical Physics
publication date: 2013-02-11T00:00:00Z
review text: The problem of whether random sampling of circulations of point vortices in Onsager's stationary statistical \(N\)-point-vortex ensemble would, in the continuum \(N\rightarrow \infty \) limit, lead to the Euler continuum vorticities predicted by the Miller-Robert theory is rigorously addressed. The analysis is performed with a view towards two-dimensional smooth manifolds, while presently specialized to random point vortices that move on the 2-sphere \(S^2\). It is proved that typical point vortex distributions obtained from the Onsager ensemble in the \(N\rightarrow \infty \) limit are special solutions of the Euler equations of an incompressible inviscid fluid flow on \(S^2\). A close affinity with the outcomes of Miller-Robert theory is established and conditions stated for the correspondence to become exact. Not addressed in the paper is a connection of the point vortex methods with two-dimensional incompressible viscous Navier-Stokes flows.
reviewed by: Piotr Garbaczewski
Mathematics Subject Classification ID: 82D15
Mathematics Subject Classification ID: 82B30
Mathematics Subject Classification ID: 76B47
Mathematics Subject Classification ID: 76Q05
Mathematics Subject Classification ID: 76F55
Mathematics Subject Classification ID: 35Q05
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 37N10
zbMATH DE Number: 6135535
zbMATH Keywords: point vortices
zbMATH Keywords: random circulations
zbMATH Keywords: vortex dynamics
zbMATH Keywords: Onsager's ensemble
zbMATH Keywords: Joyce-Montgomery mean-field theory
zbMATH Keywords: continuum limit
zbMATH Keywords: incompressible Euler fluid flow on \(S^2\)
zbMATH Keywords: turbulence
zbMATH Keywords: Miller-Robert theory
MaRDI profile type: Publication
full work available at URL: s10955-012-0552-4
OpenAlex ID: W2079124735
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Onsager's ensemble for point vortices with random circulations on the sphere (DOI)
DOI: 10.1007/S10955-012-0552-4