dissipation effect is sometimes referred to by modern authors as the ‘shear-diffusion mechanism’ and has been explicitly or implicitly pointed out by numerous authors studying shear flows [@RhinesYoung83; @LatiniBernoff01; @Chapman02; @BeckWayne11], vortex axisymmetrization [@BernoffLingevitch94; @Gilbert88; @Gilbert1993; @Bajer2001] and 3D strained vortex filaments [@Lundgren82]. The work of [@ConstantinEtAl08] considers in a more general framework the connection between the spectral properties of the background flow and the enhanced dissipation effect in the context of passive tracers using the RAGE theorem (see also [@BerestyckiHamelNadirashvili05] for the elliptic case). It is pointed out in [@BeckWayne11] that the effect can be linked to a form of ‘hypocoercivity’ [@villani2009]. Moreover, it is related to Taylor dispersion [@Taylor1953], as discussed in e.g. [@RhinesYoung83], which is not present in our work due to the periodic boundary conditions. Certain aspects of anomalous diffusions due to underlying drift have been studied in the context of SDEs; see for example [@IyerNovikov14; @YoungPumirPomeau89; @HaynesVanneste14; @CardosoTabeling88].

At high Reynolds number, the linear solution exhibits a constant flux of enstrophy to high frequencies, independent of the Reynolds number, for times $t\lesssim \textbf{Re}^{1/3}$. In [@BM13] it is shown that this enstrophy flux persists in the Euler equations. Here, we show that this enstrophy flux is 