Nonlinear Eddy-Eddy Interactions in Dry Atmospheres Macroturbulence

The statistical moment equations derived from the atmospheric equation of motions are not closed. However neglecting the large-scale eddy-eddy nonlinear interactions in an idealized dry general circulation model (GCM), which is equivalent to truncating the moment equations at the second order, can reproduce some of the features of the general circulation ([1]), highlighting the significance of eddy-mean flow interactions and the weakness of eddy-eddy interactions in atmospheric macroturbulence ([2]). The goal of the present study is to provide new insight into the rôle of these eddy-eddy interactions and discuss the relevance of a simple stochastic parametrization to represent them. We investigate in detail the general circulation in an idealized dry GCM, comparing full simulations with simulations where the eddy-eddy interactions are removed. The radiative processes are parametrized through Newtonian relaxation toward a radiative-equilibrium state with a prescribed equator to pole temperature contrast. A convection scheme relaxing toward a prescribed convective vertical lapse rate mimics some aspects of moist convection. The study is performed over a wide range of parameters covering the planetary rotation rate, the equator to pole temperature contrast and the vertical lapse rate. Particular attention is given to the wave-mean flow interactions and to the spectral budget. It is found that the no eddy-eddy simulations perform well when the baroclinic activity is weaker, for example for lower equator to pole temperature contrasts or higher rotation rates: the mean meridional circulation is well reproduced, with realistic eddy-driven jets and energy-containing eddy length scales of the order of the Rossby deformation radius. For a stronger baroclinic activity the no eddy-eddy model does not achieve a realistic isotropization of the eddies, the meridional circulation is compressed in the meridional direction and secondary eddy-driven jets emerge. In addition, the baroclinic wave activity does not reach the upper troposphere in association with a very weak or absent Rossby wave absorption in the upper subtropical troposphere. Understanding these deficiencies and the rôle of the eddy-eddy nonlinear interactions in determining the mean meridional circulation paves the way to the development of stochastic third order moments parametrizations, to eventually build GCMs that directly solve for the flow statistics and that could provide a deeper understanding of anthropogenic and natural climate changes. [1] O'Gorman, P. A., & Schneider, T. 2007, Geophysical Research Letters, 34, 22801 [2] Schneider, T., and C. C. Walker, 2006, Journal of the Atmospheric Sciences, 63, 1569-1586.