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Vanishing enstrophy dissipation in two-dimensional Navier--Stokes turbulence in the inviscid limit

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Vanishing enstrophy dissipation in two-dimensional Navier--Stokes turbulence in the inviscid limit. / Tran, Chuong Van; Dritschel, David Gerard.

In: Journal of Fluid Mechanics, Vol. 559, 25.07.2006, p. 107-116.

Research output: Contribution to journalArticle

Harvard

Tran, CV & Dritschel, DG 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

APA

Tran, C. V., & Dritschel, D. G. (2006). Vanishing enstrophy dissipation in two-dimensional Navier--Stokes turbulence in the inviscid limit. Journal of Fluid Mechanics, 559, 107-116. https://doi.org/10.1017/S0022112006000577

Vancouver

Tran CV, Dritschel DG. Vanishing enstrophy dissipation in two-dimensional Navier--Stokes turbulence in the inviscid limit. Journal of Fluid Mechanics. 2006 Jul 25;559:107-116. https://doi.org/10.1017/S0022112006000577

Author

Tran, Chuong Van ; Dritschel, David Gerard. / Vanishing enstrophy dissipation in two-dimensional Navier--Stokes turbulence in the inviscid limit. In: Journal of Fluid Mechanics. 2006 ; Vol. 559. pp. 107-116.

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@article{33224dab251e4cf4b042d1eb0742ca15,
title = "Vanishing enstrophy dissipation in two-dimensional Navier--Stokes turbulence in the inviscid limit",
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.",
keywords = "Quasi-geostrophic turbulence, Spectral distribution, Energy, Decay, Equations",
author = "Tran, {Chuong Van} and Dritschel, {David Gerard}",
year = "2006",
month = "7",
day = "25",
doi = "10.1017/S0022112006000577",
language = "English",
volume = "559",
pages = "107--116",
journal = "Journal of Fluid Mechanics",
issn = "0022-1120",
publisher = "CAMBRIDGE UNIV PRESS",

}

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TY - JOUR

T1 - Vanishing enstrophy dissipation in two-dimensional Navier--Stokes turbulence in the inviscid limit

AU - Tran, Chuong Van

AU - Dritschel, David Gerard

PY - 2006/7/25

Y1 - 2006/7/25

N2 - 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.

AB - 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.

KW - Quasi-geostrophic turbulence

KW - Spectral distribution

KW - Energy

KW - Decay

KW - Equations

UR - http://www.scopus.com/inward/record.url?scp=33746335656&partnerID=8YFLogxK

UR - http://journals.cambridge.org/action/displayIssue?iid=454619

U2 - 10.1017/S0022112006000577

DO - 10.1017/S0022112006000577

M3 - Article

VL - 559

SP - 107

EP - 116

JO - Journal of Fluid Mechanics

T2 - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -

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ID: 313519