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Published September 2007 | Published
Journal Article Open

Two-Layer Baroclinic Eddy Heat Fluxes: Zonal Flows and Energy Balance

Abstract

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, D_τ, 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^2/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) βpiv*. Existing heat-flux parameterizations, based on Kolmogorov cascade theories, predict that D_τ is nonzero and independent of κ* in the limit κ* → 0. 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 cascade theories. The convergence of these length scales is due to the formation of jet-scale eddies that align along the eastward jets. The baroclinic component of these eddies helps force the zonal mean flow, which occurs through nonzero Reynolds stress correlations in the upper layer, as opposed to the barotropic mode. This behavior suggests that the dynamics of the inverse barotropic cascade are insufficient to fully describe baroclinic turbulence.

Additional Information

© 2007 American Meteorological Society. Manuscript received 27 September 2006, in final form 13 December 2006. We thank Lien Hua and Patrice Klein for providing the spectral code used in this work. We have benefited from conversations with Paola Cessi, Rick Salmon, Isaac Held, Guillaume Lapeyre, Geoff Vallis, Shaffer Smith, and Boris Galperin. This work was supported by National Science Foundation Grants OCE-0220362 and OCE-0100868. A. F. Thompson also gratefully acknowledges the support of an NDSEG Fellowship.

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August 22, 2023
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