Scaling baroclinic eddy fluxes: Vortices and energy balance

The eddy heat flux generated by the statistically equilibrated baroclinic instability of a uniform, horizontal temperature gradient is studied using a two-mode f-plane quasigeostrophic model. An overview of the dependence of the eddy diffusivity D on the bottom friction kappa, the deformation radius lambda, the vertical variation of the large-scale flow U, and the domain size L is provided by numerical simulations at 70 different values of the two nondimensional control parameters kappa lambda/U and L/lambda. Strong, axisymmetric, well-separated baroclinic vortices dominate both the barotropic vorticity and the temperature fields. The core radius of a single vortex is significantly larger than lambda but smaller than the eddy mixing length l(mix). On the other hand, the typical vortex separation is comparable to l(mix). Anticyclonic vortices are hot, and cyclonic vortices are cold. The motion of a single vortex is due to barotropic advection by other distant vortices, and the eddy heat flux is due to the systematic migration of hot anticyclones northward and cold cyclones southward. These features can be explained by scaling arguments and an analysis of the statistically steady energy balance. These arguments result in a relation between D and l(mix). Earlier scaling theories based on coupled Kolmogorovian cascades do not account for these coherent structures and are shown to be unreliable. All of the major properties of this dilute vortex gas are exponentially sensitive to the strength of the bottom drag. As the bottom drag decreases, both the vortex cores and the vortex separation become larger. Provided that l(mix) remains significantly smaller than the domain size, then local mixing length arguments are applicable, and our main empirical result is l(mix) approximate to 4 lambda exp(0.3U/kappa lambda).