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Vanishing enstrophy dissipation in two-dimensional Navier--Stokes turbulence in the inviscid limit
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dc.contributor.author | Tran, Chuong Van | |
dc.contributor.author | Dritschel, David Gerard | |
dc.date.accessioned | 2010-12-01T15:56:57Z | |
dc.date.available | 2010-12-01T15:56:57Z | |
dc.date.issued | 2006-07-25 | |
dc.identifier.citation | Tran , 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 . https://doi.org/10.1017/S0022112006000577 | en |
dc.identifier.issn | 0022-1120 | |
dc.identifier.other | PURE: 313519 | |
dc.identifier.other | PURE UUID: 33224dab-251e-4cf4-b042-d1eb0742ca15 | |
dc.identifier.other | WOS: 000239832400005 | |
dc.identifier.other | Scopus: 33746335656 | |
dc.identifier.other | ORCID: /0000-0002-1790-8280/work/61133270 | |
dc.identifier.other | ORCID: /0000-0001-6489-3395/work/64697750 | |
dc.identifier.uri | https://hdl.handle.net/10023/1564 | |
dc.description.abstract | Batchelor (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.format.extent | 10 | |
dc.language.iso | eng | |
dc.relation.ispartof | Journal of Fluid Mechanics | en |
dc.rights | (c)2006 Cambridge University Press | en |
dc.subject | Quasi-geostrophic turbulence | en |
dc.subject | Spectral distribution | en |
dc.subject | Energy | en |
dc.subject | Decay | en |
dc.subject | Equations | en |
dc.subject | QA Mathematics | en |
dc.subject.lcc | QA | en |
dc.title | Vanishing enstrophy dissipation in two-dimensional Navier--Stokes turbulence in the inviscid limit | en |
dc.type | Journal article | en |
dc.description.version | Publisher PDF | en |
dc.contributor.institution | University of St Andrews. Applied Mathematics | en |
dc.identifier.doi | https://doi.org/10.1017/S0022112006000577 | |
dc.description.status | Peer reviewed | en |
dc.identifier.url | http://www.scopus.com/inward/record.url?scp=33746335656&partnerID=8YFLogxK | en |
dc.identifier.url | http://journals.cambridge.org/action/displayIssue?iid=454619 | en |
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