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

Chuong Van Tran, David Gerard Dritschel

Research output: Contribution to journalArticlepeer-review

32 Citations (Scopus)


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.

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


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


Dive into the research topics of 'Vanishing enstrophy dissipation in two-dimensional Navier--Stokes turbulence in the inviscid limit'. Together they form a unique fingerprint.

Cite this