Quantitatively mapping the Eady model onto a two-layer quasi-geostrophic model

The two-layer quasi-geostrophic (2LQG) model and the Eady model are two idealised systems illustrating the baroclinic instability of atmospheric jets and ocean currents. The two set-ups share many ingredients – background vertically sheared zonal flow of density-stratified fluid in a rapidly rotating frame – while differing in complexity and dimensionality. The Eady model has a continuous vertical direction, with baroclinic turbulence induced by boundary potential vorticity (PV) gradients at top and bottom. By contrast, the 2LQG sytem typically models baroclinic instability induced by interior PV gradients. This distinction challenges our ability to clearly identify a couple of ‘modes’ through which the Eady dynamics could be inferred from a simpler 2LQG system. In the present study, we show that this difficulty can be circumvented in the turbulent regime arising for weak bottom drag. Namely, guided by the common organisation of both systems into a gas of coherent vortices, we identify a quantitative mapping between the Eady and 2LQG models. The mapping allows for parameter-free predictions of the eddy diffusivity of the Eady model based on knowledge of the 2LQG diffusivity. We illustrate these results using numerical simulations of the Eady and 2LQG models with linear or quadratic bottom drag.