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The effect of asymmetric large-scale dissipation on energy and potential enstrophy injection in two-layer quasi-geostrophic turbulenceAbstract: In the Nastrom-Gage spectrum of atmospheric turbulence we observe a $k^{-3}$ energy spectrum that transitions into a $k^{-5/3}$ spectrum with increasing wavenumber $k$. The transition occurs near a transition wavenumber $k_t$ located near the Rossby deformation wavenumber $k_R$. The Tung-Orlando theory interprets this spectrum as a double downscale cascade of potential enstrophy and energy, from large scales to small scales. We show that in a temperature forced two-layer quasi-geostrophic model, the rates with which potential enstrophy and energy are injected places the transition wavenumber $k_t$ near $k_R$, as long as most potential enstrophy and energy cascade to small scales. We also show that, contrary to what occurs in two-dimensional turbulence, the effect of asymmetric Ekman damping is to intensify the energy flux in the subleading downscale energy cascade and it may increase or decrease the flux of the downscale potential enstrophy cascade depending on the distribution of energy between kinetic and potential energy for the forcing range wavenumbers. Using a random gaussian forcing model we also show that suppressing the bottom layer forcing term decreases the ratio $\gn/\gee$ of injected potential enstrophy over injected energy thereby tending to decrease kt further. Based on these results we argue that the Tung-Orlando theory can account for the approximate coincidence between $k_t$ and $k_R$. |