@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", }