## 1. Introduction

[2] The study of turbulent flows has focused on idealized isotropic and homogeneous geometries in which mean flows vanish and nonlinear interactions among eddies are of central importance in determining the higher-order flow statistics [*McComb*, 1992]. Large-scale (>500 km) turbulence in the atmosphere is an example of turbulent flow in which other effects such as interactions of eddies with the mean flow are important, and for which, as the results presented here suggest, a focus on nonlinear eddy-eddy interactions may be inappropriate. The most energetic transient eddies in the atmosphere—the familiar cyclones and anticyclones—have a length scale of ∼3000 km [*Shepherd*, 1987; *Straus and Ditlevsen*, 1999]. Baroclinic instability is the main energy source for these eddies, and the length scale of the linearly most unstable wave (given by the Rossby deformation radius) and the energy-containing eddy length scale are of similar magnitude. The inverse eddy energy cascade to length scales much larger than the Rossby deformation radius that can occur in two-dimensional or quasigeostrophic models is not seen in the atmosphere, although energy transfer from eddies to the zonal-mean flow at scales larger than the Rossby deformation radius does occur [*Shepherd*, 1987]. Simulations and theory suggest that the absence of this kind of inverse energy cascade is not an accident but comes about through the effect of the eddies on the mean thermal structure of the atmosphere [*Schneider and Walker*, 2006]. Thus, nonlinear eddy-eddy interactions (e.g., the advection of eddy fluctuations in temperature by eddy fluctuations in the wind), which could lead to an inverse energy cascade, may be relatively unimportant in determining the energy-containing length scale of atmospheric eddies.

[3] Eddy-eddy interactions are also commonly invoked to explain the shape of the atmospheric eddy kinetic energy spectrum, which has an approximate *n*^{−3} power-law range in spherical wavenumber *n* at length scales smaller than the energy-containing eddy length scale [*Boer and Shepherd*, 1983; *Nastrom and Gage*, 1985; *Straus and Ditlevsen*, 1999; *Schneider and Walker*, 2006]. The *n*^{−3} range is commonly explained by analogy with two-dimensional or quasigeostrophic models of atmospheric flow, which can exhibit an enstrophy cascade with an *n*^{−3} energy spectrum [*Charney*, 1971; *Salmon*, 1998]. Enstrophy is proportional to the mean-square vorticity (in two dimensional models) or potential vorticity (in quasigeostrophic models), and inertial-range cascades involving eddy-eddy interactions are postulated for it and the kinetic energy because they are both quadratic invariants of the inviscid flow [*Kraichnan*, 1967]. An *n*^{−3} spectrum might also be expected over a wavenumber range in which vorticity or potential vorticity is effectively advected as a passive scalar. Such an energy spectrum is sufficiently steep that spectrally nonlocal eddy-eddy interactions may be important (such as strain of small-scale vorticity by large-scale eddies), leading to a logarithmic correction to the power-law spectrum [*Kraichnan*, 1971; *Salmon*, 1998]. In the atmosphere, however, an inertial range in which only eddy-eddy interactions are important does not occur. Other terms such as conversion from potential to kinetic energy, transfer of energy to the mean flow, and eddy dissipation (primarily in the planetary boundary layer) are known to be important in the spectral energy budget over a range of length scales [*Lambert*, 1987; *Straus and Ditlevsen*, 1999]. Thus, it is not clear why the energy spectrum of the atmosphere should follow an *n*^{−3} power law, and the enstrophy-cascade explanation for the atmospheric energy spectrum has been questioned [*Vallis*, 1992]. Furthermore, the baroclinic lifecycle experiments of *Gall* [1976] suggest (albeit indirectly) that the shape of the energy spectrum may not depend on eddy-eddy interactions.

[4] Rather than studying the processes that determine the mean state and energy spectrum in two-dimensional or quasigeostrophic systems, we use an atmospheric general circulation model (GCM), which more faithfully resolves the large-scale turbulence of the atmosphere by representing all important terms in the spectral energy budget and by allowing for dynamical changes in the thermal stratification. In removing the eddy-eddy interactions in a GCM, we directly test their role in determining the eddy length scale, the eddy energy spectrum of atmospheric turbulence, and the general circulation of the atmosphere. The removal of eddy-eddy interactions represents a turbulence closure equivalent to a truncation of the moment equations at second order by setting third-order eddy moments (third-order cumulants) to zero [*Herring*, 1963; *Marston et al.*, 2007]. While we eliminate the nonlinear interactions that involve only eddies, we do retain the effects of eddies on the mean flow because of the important role of eddy heat and momentum fluxes in equilibrating the mean flow.