The Effect of Asymmetric Ekman Damping on Energy and Enstrophy Injection in Two-layer Quasi-geostrophic Turbulence

An analysis of wind and temperature measurements taken during the Global Atmospheric Sampling Program by Nastrom and Gage showed that there is a robust k^-3 energy spectrum extending from approximately 3,000 km to 1,000 km in wavelength and a robust k^-5/3 energy spectrum extending from 600 km down to a few kilometers. Tung and Orlando have demonstrated numerically that the two-layer quasi-geostrophic model, forced at large scales by baroclinic instability can reproduce this energy spectrum as a combined downscale enstrophy and energy cascade. However, their result is considered, by some, to be controversial. More detailed models have been shown to reproduce the Nastrom-Gage energy spectrum as well. However, the question remains: what is the simplest model that can account for the Nastrom-Gage spectrum?
In this talk I will present the recent progress that has been made towards addressing this question. First, we will argue that, contrary to the case of two-dimensional turbulence where the downscale energy flux is constrained to vanish rapidly with increasing scale separation, in the two-layer QG model, asymmetric dissipation loosens this constraint thereby allowing an inertial range transition from $k^{-3}$ scaling to $k^{-5/3}$ scaling. Furthermore, we have shown that in the two-layer QG model energy and enstrophy are injected at a proportion that places the transition wavenumber near the Rossby wavenumber in agreement with observation. Finally, we show that the effect of asymmetric Ekman damping at the forcing range is to decrease the rate of enstrophy injection as well as the ratio of enstrophy to energy injection, thus tending to decrease the transition wavenumber further.