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dc.contributor.authorDritschel, David Gerard
dc.contributor.authorTran, Chuong Van
dc.contributor.authorScott, Richard Kirkness
dc.identifier.citationDritschel , D G , Tran , C V & Scott , R K 2007 , ' Revisiting Batchelor's theory of two-dimensional turbulence ' , Journal of Fluid Mechanics , vol. 591 , pp. 379-391 .
dc.identifier.otherPURE: 397186
dc.identifier.otherPURE UUID: d99be448-835f-4bc0-9f6f-104f290bc772
dc.identifier.otherWOS: 000251474500015
dc.identifier.otherScopus: 40449132762
dc.identifier.otherORCID: /0000-0001-5624-5128/work/55378698
dc.identifier.otherORCID: /0000-0002-1790-8280/work/61133267
dc.identifier.otherORCID: /0000-0001-6489-3395/work/64697745
dc.description.abstractRecent mathematical results have shown that a central assumption in the theory of two-dimensional turbulence proposed by Batchelor (Phys. Fluids, vol. 12, 1969, p. 233) is false. That theory, which predicts a X-2/3 k(-1) enstrophy spectrum in the inertial range of freely-decaying turbulence, and which has evidently been successful in describing certain aspects of numerical simulations at high Reynolds numbers Re, assumes that there is a finite, non-zero enstrophy dissipation X in the limit of infinite Re. This, however, is not true for flows having finite vorticity. The enstrophy dissipation in fact vanishes. We revisit Batchelor's theory and propose a simple modification of it to ensure vanishing X in the limit Re -> infinity. Our proposal is supported by high Reynolds number simulations which confirm that X decays like 1/ln Re, and which, following the time of peak enstrophy dissipation, exhibit enstrophy spectra containing an increasing proportion of the total enstrophy (omega(2))/2 in the inertial range as Re increases. Together with the mathematical analysis of vanishing X, these observations motivate a straightforward and, indeed, alarmingly simple modification of Batchelor's theory: just replace Batchelor's enstrophy spectrum X(2/3)k(-1) with (omega(2))k(-1)(In Re)(-1).
dc.relation.ispartofJournal of Fluid Mechanicsen
dc.rights(c)2007 Cambridge University Pressen
dc.subjectDimensional decaying turbulenceen
dc.subjectEuler equationsen
dc.subjectEnstrophy dissipationen
dc.subjectContour dynamicsen
dc.subjectQA Mathematicsen
dc.titleRevisiting Batchelor's theory of two-dimensional turbulenceen
dc.typeJournal articleen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. Applied Mathematicsen
dc.description.statusPeer revieweden

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