We thank Alan Plumb, John Marshall, and Ryan Abernathey for helpful comments and discussions. This work was supported through NSF Award OCE-0849233.
Andrews, D. G., , J. R. Holton, , and C. B. Leovy, 1987: Middle Atmosphere Dynamics. International Geophysics Series, Vol. 40, Academic Press, 489 pp.
Barry, L., , G. C. Craig, , and J. Thuburn, 2000: A GCM investigation into the nature of baroclinic adjustment. J. Atmos. Sci., 57, 1141–1155.
Green, J. S. A., 1970: Transfer properties of the large-scale eddies and the general circulation of the atmosphere. Quart. J. Roy. Meteor. Soc., 96, 157–185.
Haynes, P., , and E. Shuckburgh, 2000: Effective diffusivity as a diagnostic of atmospheric transport: 2. Troposphere and lower stratosphere. J. Geophys. Res., 105 (D18), 22 795–22 810.
Held, I. M., 1978: The vertical scale of an unstable baroclinic wave and its importance for eddy heat flux parameterizations. J. Atmos. Sci., 35, 572–576.
Jansen, M., 2012: Equilibration of an atmosphere by geostrophic turbulence. Ph.D. dissertation, Massachusetts Institute of Technology, 187 pp.
Jansen, M., , and R. Ferrari, 2012: Macroturbulent equilibration in a thermally forced primitive equation system. J. Atmos. Sci., 69, 695–713.
Juckes, M. N., , I. N. James, , and M. Blackburn, 1994: The influence of Antarctica on the momentum budget of the southern extratropics. Quart. J. Roy. Meteor. Soc., 120, 1017–1044.
Koh, T.-Y., , and R. A. Plumb, 2004: Isentropic zonal average formalism and the near-surface circulation. Quart. J. Roy. Meteor. Soc., 130, 1631–1653.
Marshall, J. C., , C. Hill, , L. Perelman, , and A. Adcroft, 1997: Hydrostatic, quasi-hydrostatic, and nonhydrostatic ocean modeling. J. Geophys. Res., 102 (C3), 5753–5766.
Phillips, N. A., 1954: Energy transformations and meridional circulations associated with simple baroclinic waves in a two-level, quasi-geostrophic model. Tellus, 6, 273–286.
Plumb, R., , and J. Mahlman, 1987: The zonally averaged transport characteristics of the GFDL general circulation/transport model. J. Atmos. Sci., 44, 298–327.
Schneider, T., 2004: The tropopause and the thermal stratification in the extratropics of a dry atmosphere. J. Atmos. Sci., 61, 1317–1340.
Schneider, T., 2005: Zonal momentum balance, potential vorticity dynamics, and mass fluxes on near-surface isentropes. J. Atmos. Sci., 62, 1884–1900.
Schneider, T., , and C. C. Walker, 2006: Self-organization of atmospheric macroturbulence into critical states of weak nonlinear eddy–eddy interactions. J. Atmos. Sci., 63, 1569–1586.
Vallis, G. K., 2006: Atmospheric and Oceanic Fluid Dynamics. Cambridge University Press, 745 pp.
Zurita-Gotor, P., , and G. K. Vallis, 2010: Circulation sensitivity to heating in a simple model of baroclinic turbulence. J. Atmos. Sci., 67, 1543–1558.
Notice that the theoretical discussions above are for the more general case of a compressible fluid, in direct analogy to the derivations in Schneider (2004) and Koh and Plumb (2004). However, as discussed in Jansen and Ferrari (2012), the same results are obtained in the Boussinesq limit.
Notice that the surface eddy diffusivity is here calculated using the actual surface potential temperature flux. Following the full derivation shown in Schneider (2005), or Koh and Plumb (2004), the surface term in Eqs. (14) and (15) should generally be described by the geostrophic eddy flux of surface potential temperature. In the presented simulation, where the Rossby number is small and no enhanced surface drag is used, the difference between the full eddy flux and the geostrophic eddy flux is negligible.
The conservation equation for the generalized thickness [Eq. (A3)] can be derived from the conservation equations for thickness ∂tσ + ∇θ · (uσ) = 0 (e.g., Andrews et al. 1987) and the thermodynamic equation for surface potential temperature ∂tθs + u · ∇θs = 0.