Two-layer baroclinic eddy heat fluxes: zonal flows and energy balance

The eddy heat flux generated by statistically equilibrated baroclinic turbulence supported on a uniform, horizontal temperature gradient is examined using a two-layer β-plane quasigeostrophic model. The dependence of the eddy diffusivity of temperature, Dτ , on external parameters such as β, bottom friction κ, the deformation radius λ and the velocity jump 2U is provided by numerical simulations at 110 different points in the parameter space β∗ = βλ /U and κ∗ = κλ/U . There is a special “pivot” value of β∗, β piv ∗ ≈ 11/16, at which Dτ depends weakly on κ∗. But otherwise Dτ has a complicated dependence on both β∗ and κ∗, highlighted by the fact that reducing κ∗ leads to increases (decreases) in Dτ if β is less than (greater than) β ∗ . Existing heat-flux parameterizations, based on Kolmogorovian cascade theories, predict that Dτ is nonzero and independent of κ∗ in the limit κ∗ → 0. Our simulations show indications of this regime provided that κ∗ ≤ 0.04 and 0.25 ≤ β∗ ≤ 0.5. All important length scales in this problem, namely the mixing length, the scale of the energy containing eddies, the Rhines scale and the spacing of the zonal jets, converge to a common value as bottom friction is reduced. The mixing length and jet spacing do not decouple in the parameter regime considered here, as predicted by