a corrected proof given by @article:Tung:2005:1. However, as was shown by [@article:Tung:2007], this result is not necessarily generalizable to quasi-geostrophic models. Thus, @article:Smith:2004 did not establish the claim that “an inertial range transition is not possible in quasi-geostrophic models”, and the theoretical problem remains open. (d) Since the diagnostics of the Tung-Orlando simulation indicate that the downscale energy dissipation rate balances the rate with which energy is sent downscale from the forcing range, the simulation is sufficiently well-resolved to prevent a bottleneck-type energy pile up at small scales, over a time-scale longer than the runtime of the simulation.

Be that as it may, the underlying theoretical question, implied by @article:Smith:2004, remained open: How can the downscale energy flux $\gee$ be large enough to yield a gap between $k_t$ and $k_d$, when that is not possible in two-dimensional turbulence? An even deeper question also demanded further understanding: how is it possible for two downscale cascades to coexist? These lingering questions generated skepticism towards the Tung-Orlando theory, which is why we were prompted to investigate them at greater depth. In @article:Tung:2005 [@article:Tung:2005:1], we augmented the Tung-Orlando theory by noting that even in two-dimensional turbulence there is a small amount of energy cascading 