the same dynamical behaviour as two-dimensional turbulence, where, according to the theory of @article:Kraichnan:1967:1, @article:Leith:1968, and @article:Batchelor:1969, there is a downscale enstrophy cascade and an upscale inverse energy cascade. This assumption follows from @article:Charney:1971 who claimed that there is an “isomorphism” between quasi-geostrophic turbulence and two-dimensional turbulence. More recently, key differences between these two models were noted by [@article:Welch:2001], @article:Orlando:2003:1, and @article:Tung:2007. The most remarkable difference was highlighted in the numerical simulation of the two-layer quasi-geostrophic model by @article:Orlando:2003, which produced an energy spectrum that scales as $k^{-3}$ initially, and with increasing wavenumber $k$, transitions to $k^{-5/3}$ scaling. This is consistent with the observed energy spectrum of the atmosphere, as was first measured by @article:Gage:1984 and @article:Nastrom:1986, but it is inconsistent with our conventional understanding of the dynamical behavior of two-dimensional turbulence, as described by the theory of @article:Kraichnan:1967:1, @article:Leith:1968, and @article:Batchelor:1969. @article:Orlando:2003 showed that their simulation produced a downscale enstrophy cascade that co-existed with a downscale energy cascade, with both energy and enstrophy injected by baroclinic instability at small wavenumbers, and dissipated at large wavenumbers. If $\gn$ is the enstrophy flux and $\gee$ is the energy flux associated with these coexisting cascades, then, by dimensional analysis, @article:Orlando:2003 argue that 