  We numerically and theoretically investigate the Boussinesq Eady model, where
a rapidly rotating density-stratified layer of fluid is subject to a meridional
temperature gradient in thermal wind balance with a uniform vertically sheared
zonal flow. Through a suite of numerical simulations, we show that the
transport properties of the resulting turbulent flow are governed by
quasi-geostrophic (QG) dynamics in the rapidly rotating strongly stratified
regime. The 'vortex gas' scaling predictions put forward in the context of the
two-layer QG model carry over to this fully 3D system: the functional
dependence of the meridional flux on the control parameters is the same, the
two ajustable parameters entering the theory taking slightly different values.
In line with the QG prediction, the meridional buoyancy flux is
depth-independent. The vertical buoyancy flux is such that turbulence
transports buoyancy along isopycnals, except in narrow layers near the the top
and bottom boundaries, the thickness of which decreases as the diffusivities go
to zero. The emergent (re)stratification is set by a simple balance between the
vertical buoyancy flux and diffusion along the vertical direction. Overall,
this study demonstrates how the vortex-gas scaling theory can be adapted to
quantitatively predict the magnitude and vertical structure of the meridional
and vertical buoyancy fluxes, and of the emergent stratification, without
additional fitting parameters.
