stable in the inviscid limit, and moreover gives rise to the enhanced dissipation. It is suggested in [@Lundgren82; @Gilbert88; @Gilbert1993; @GilbertBassom98], that the inviscid limit of this enhanced dissipation effect is important for understanding the fine scale features of turbulent flows predicted in Kolmogorov [@Kolmogorov1941] and Batchelor/Kraichnan [@Batchelor1969; @Kraichnan67] theories. However, notice that the constant enstrophy flux in is [*more efficient*]{} than a [*generic turbulent flow*]{} at moving enstrophy to small scales (where it is annihilated by the diffusion). Indeed, one can see this by considering the associated dissipative length scale $\ell_D$. Since the enstrophy transfer is linear in time, we see that in fact $\ell_D \sim {\textbf{Re}}^{-1/3}$ which is a much larger scale than the $\textbf{Re}^{-1/2}$ predicted by the Kraichnan statistical theory. Partly, this is due to the fact that the enstrophy transfer considered here is highly anisotropic, and so should not necessarily be in the same scaling regime as homogeneous, isotropic turbulence.

It is well known that studying the inviscid limit $\nu \to 0$ and setting $\nu = 0$ in is not the same problem. Theorem \[thm:Main\] below (and [@BM13]) implies that the 2D Euler equations qualitatively predict the correct behavior of for times $t \lesssim \textbf{Re}^{1/3}$, at 