Skip to content

Research at St Andrews

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

Research output: Contribution to journalArticle

Author(s)

School/Research organisations

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.

Close

Details

Original languageEnglish
Pages (from-to)107-116
Number of pages10
JournalJournal of Fluid Mechanics
Volume559
DOIs
Publication statusPublished - 25 Jul 2006

    Research areas

  • Quasi-geostrophic turbulence, Spectral distribution, Energy, Decay, Equations

Discover related content
Find related publications, people, projects and more using interactive charts.

View graph of relations

Related by author

  1. Energy dissipation and resolution of steep gradients in one-dimensional Burgers flows

    Tran, C. V. & Dritschel, D. G., Mar 2010, In : Physics of Fluids. 22, 3, 7 p., 037102.

    Research output: Contribution to journalArticle

  2. Late time evolution of unforced inviscid two-dimensional turbulence

    Dritschel, D. G., Scott, R. K., Macaskill, C., Gottwald, G. & Tran, C. V., 2009, In : Journal of Fluid Mechanics. 640, p. 215-233 19 p.

    Research output: Contribution to journalArticle

  3. Unifying scaling theory for vortex dynamics in two-dimensional turbulence

    Dritschel, D. G., Scott, R. K., Macaskill, C., Gottwald, G. A. & Tran, C. V., 29 Aug 2008, In : Physical Review Letters. 101, 9, 4 p., 094501.

    Research output: Contribution to journalArticle

  4. Revisiting Batchelor's theory of two-dimensional turbulence

    Dritschel, D. G., Tran, C. V. & Scott, R. K., 25 Nov 2007, In : Journal of Fluid Mechanics. 591, p. 379-391 13 p.

    Research output: Contribution to journalArticle

Related by journal

  1. On the regularity of the Green-Naghdi equations for a rotating shallow fluid layer

    Dritschel, D. G. & Jalali, M. R., 25 Apr 2019, In : Journal of Fluid Mechanics. 865, p. 100-136

    Research output: Contribution to journalArticle

  2. Scale-invariant singularity of the surface quasigeostrophic patch

    Scott, R. K. & Dritschel, D. G., 25 Mar 2019, In : Journal of Fluid Mechanics. 863, 12 p., R2.

    Research output: Contribution to journalArticle

  3. The stability and nonlinear evolution of quasi-geostrophic toroidal vortices

    Reinaud, J. N. & Dritschel, D. G., 25 Mar 2019, In : Journal of Fluid Mechanics. 863, p. 60-78

    Research output: Contribution to journalArticle

  4. Three-dimensional quasi-geostrophic vortex equilibria with m−fold symmetry

    Reinaud, J. N., 25 Mar 2019, In : Journal of Fluid Mechanics. 863, p. 32-59

    Research output: Contribution to journalArticle

Related by journal

  1. Journal of Fluid Mechanics (Journal)

    David Gerard Dritschel (Editor)
    2005 → …

    Activity: Publication peer-review and editorial work typesEditor of research journal

ID: 313519