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Title: Vanishing enstrophy dissipation in two-dimensional Navier--Stokes turbulence in the inviscid limit
Authors: Tran, Chuong Van
Dritschel, David Gerard
Keywords: Quasi-geostrophic turbulence
Spectral distribution
Energy
Decay
Equations
QA Mathematics
Issue Date: 25-Jul-2006
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 .
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.
Version: Publisher PDF
Status: Peer reviewed
URI: http://hdl.handle.net/10023/1564
http://journals.cambridge.org/action/displayIssue?iid=454619
DOI: http://dx.doi.org/10.1017/S0022112006000577
ISSN: 0022-1120
Type: Journal article
Rights: (c)2006 Cambridge University Press
Appears in Collections:University of St Andrews Research
Applied Mathematics Research



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