Eddy equilibration in idealized models of the extratropical troposphere

Abstract

The equilibration of the extratropical troposphere is controlled in large part by the transient eddy heat fluxes. This thesis analyzes some idealized models that capture the essential sources of complexity which have hindered our understanding of these fluxes. In particular, it attempts to eliminate some knowledge gaps between proposed turbulence diffusivity theories for these fluxes.

The thesis begins by comparing two of these theories, one motivated by homogeneous quasigeostrophic (QG) simulations and one by parameter variations in a comprehensive atmospheric model. The two theories share the same turbulent inverse energy cascade argument but differ in the assumptions concerning the mixing slope used in estimating the entropy budget. The importance of this mixing slope is verified using an idealized dry general circulation model (GCM).

We find that the inverse cascade part of these theories fails to explain some of the GCM simulations. Hence, we return to the homogeneous two-layer QG model. In the limit of vanishing environmental vorticity gradient 𝛽=0, we find that the diffusivity does not depend on the friction in the same way as the passive tracer diffusivity in barotropic turbulence. Unlike what is typically assumed, there is no classical inverse cascade inertial range in the two-layer model.

We next show that the 𝛽 dependence of heat flux diffusivity can be combined with the dependence on friction in a single nondimensional parameter. Based on this result, we discuss how the heat flux diffusivity is suppressed by 𝛽 due to wave propagation in addition to its effect on the extent of the inverse cascade.

Finally, we return to the idealized GCM to evaluate the maximum entropy production (MEP) argument, which suggests that the eddy heat fluxes adjust to maintain the MEP state. We solve for the MEP climate and show that it is unlikely to be physically relevant even if one constrains the global mean vertical temperature profile. We argue against the use of the MEP argument and reaffirm the need to thoroughly understand the eddy dynamics.