a downscale energy cascade, thereby vindicating the fundamental premise of the Tung-Orlando theory. A further advantage of the Tulloch-Smith QG model is that it seems to have resolved the small-scale energy dissipation sink problem implied by the HVK argument of @article:Smith:2004. Since the Tulloch-Smith QG model is still a severely restricted approximation of the full quasi-geostrophic model, it is reasonable to expect that the small-scale energy dissipation sink problem will remain resolved under the full quasi-geostrophic model. This raises many interesting questions that are, unfortunately, beyond the scope of this paper, but will be investigated in future work.

The goal of the present paper is to add one more piece to the overall puzzle by looking at the forcing range instead of the dissipation range. We will thus consider the effect of symmetric versus asymmetric forcing on the dynamics of the two-layer quasi-geostrophic model. We will first show that when the model is forced exclusively through the temperature equation, this results in antisymmetric forcing on the potential vorticity equations for both layers. Consequently, the energy forcing spectrum $F_E(k)$ and the potential enstrophy forcing spectrum $F_G(k)$ are related as $F_G(k) = (k^2+k_R^2) F_E(k)$, with $k_R$ the Rossby wavenumber. For forcing-range wavenumbers 