the transition from $k^{-3}$ scaling to $k^{-5/3}$ scaling should occur at a transition wavenumber $k_t \sim (\gn/\gee)^{1/2}$, and it does.

This result bolstered the Tung-Orlando theory that interpreted the Nastrom-Gage spectrum as a coexisting downscale potential enstrophy cascade and downscale energy cascade, both spanning a comparable range of length scales. It should be noted that it was not the intention of @article:Orlando:2003 to claim that the entire Nastrom-Gage spectrum can be explained via the two-layer quasi-geostrophic model. The point of the simulation was to demonstrate that it is possible to have coexisting downscale potential enstrophy and energy cascades, even in models as close to two-dimensional turbulence as the two-layer quasi-geostrophic model. This possibility is bound to become even more favorable under models that are further away from the two-dimensional approximation, such as the multi-layer quasi-geostrophic model or the three-dimensional stratified turbulence model. Gravity waves can also play a helpful role in facilitating coexisting cascades, as discussed further in section 5.

In a subsequent paper, @article:Smith:2004 criticized @article:Orlando:2003 on the following grounds: First, using his “HVK scale” estimates, he claimed that the Tung-Orlando numerical simulation is not well-resolved and that therefore the $k^{-5/3}$ part of the Tung-Orlando energy spectrum is a 