bottleneck instead of being indicative of a real cascade. In connection with this claim, @article:Smith:2004 criticized the use of a resolution-dependent hyperdiffusion coefficient by @article:Orlando:2003. Second, that in two-dimensional turbulence it is not possible for the downscale energy flux to be large enough to create a gap between the transition wavenumber $k_t$ and the dissipation wavenumber $k_d$. In response, @article:Tung:2004 noted that: (a) Since, the diagnostics in the Tung-Orlando simulation indicate a downscale enstrophy flux $\gn$ and a downscale energy flux $\gee$ that have magnitudes consistent with the location of the transition wavenumber $k_t$ in the simulation’s energy spectrum, it is very unlikely that the transition is caused by an energy bottleneck, as argued by @article:Smith:2004. (b) The use of a resolution-dependent hyperviscosity coefficient is intended to model the anomalous energy dissipation sink at small scales, originating from three-dimensional dynamics, by controlling the downscale energy dissipation rate. (c) Smith’s “HVK scale” argument, which was used to argue that the Tung-Orlando simulation is not well-resolved, has various flaws, discussed in detail by @article:Tung:2004, that render it inconclusive. Nevertheless, Smith’s claim, that $k_t$ will coincide with the dissipation scale $k_d$, can be shown to hold, for the case of two-dimensional turbulence, via 