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dc.contributor.authorTran, Chuong Van
dc.contributor.authorDritschel, David Gerard
dc.identifier.citationTran , C V & Dritschel , D G 2006 , ' Vanishing enstrophy dissipation in two-dimensional Navier--Stokes turbulence in the inviscid limit ' , Journal of Fluid Mechanics , vol. 559 , pp. 107-116 .
dc.identifier.otherPURE: 313519
dc.identifier.otherPURE UUID: 33224dab-251e-4cf4-b042-d1eb0742ca15
dc.identifier.otherWOS: 000239832400005
dc.identifier.otherScopus: 33746335656
dc.identifier.otherORCID: /0000-0002-1790-8280/work/61133270
dc.identifier.otherORCID: /0000-0001-6489-3395/work/64697750
dc.description.abstractBatchelor (Phys. Fluids, vol. 12, 1969, p. 233) developed a theory of two-dimensional turbulence based on the assumption that the dissipation of enstrophy (mean-square vorticity) tends to a finite non-zero constant in the limit of infinite Reynolds number Re. Here, by assuming power-law spectra, including the one predicted by Batchelor's theory, we prove that the maximum dissipation of enstrophy is in fact zero in this limit. Specifically, as Re -> infinity, the dissipation approaches zero no slower than (ln Re)(-1/2). The physical reason behind this result is that the decrease of viscosity enhances the production of both palinstrophy (mean-square vorticity gradients) and its dissipation - but in such a way that the net growth of palinstrophy is less rapid than the decrease of viscosity, resulting in vanishing enstrophy dissipation. This result generalizes to a rich class of quasi-geostrophic models as well as to the case of a passive tracer in layerwise-two-dimensional turbulent flows having bounded enstrophy.
dc.relation.ispartofJournal of Fluid Mechanicsen
dc.rights(c)2006 Cambridge University Pressen
dc.subjectQuasi-geostrophic turbulenceen
dc.subjectSpectral distributionen
dc.subjectQA Mathematicsen
dc.titleVanishing enstrophy dissipation in two-dimensional Navier--Stokes turbulence in the inviscid limiten
dc.typeJournal articleen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews.Applied Mathematicsen
dc.description.statusPeer revieweden

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