A parameterization of mesoscale eddy fluxes in the ocean should be consistent with the fact that the ocean interior is nearly adiabatic. Gent and McWilliams have described a framework in which this can be approximated in z-coordinate primitive equation models by incorporating the effects of eddies on the buoyancy field through an eddy-induced velocity. It is also natural to base a parameterization on the simple picture of the mixing of potential vorticity in the interior and the mixing of buoyancy at the surface. The authors discuss the various constraints imposed by these two requirements and attempt to clarify the appropriate boundary conditions on the eddy-induced velocities at the surface. Quasigeostrophic theory is used as a guide to the simplest way of satisfying these constraints.

The scaling argument developed by Larichev and Held (1995) for eddy amplitudes and fluxes in a horizontally homogeneous, two-layer model on an f -plane is extended to a β-plane. In terms of the non-dimensional number ξ = U/(βλ 2 ), where λ is the deformation radius and U is the mean thermal wind, the result for the RMS eddy velocity V , the characteristic wavenumber of the energy-containing eddies and of the eddy-driven jets k j , and the magnitude of the eddy diffusivity for potential vorticity D, in the limit ξ ≫ 1, are as follows:

This paper considers the requirements that must be satisfied in order to provide a stable and physically based isoneutral tracer diffusion scheme in a z-coordinate ocean model. Two properties are emphasized: 1) downgradient orientation of the diffusive fluxes along the neutral directions and 2) zero isoneutral diffusive flux of locally referenced potential density. It is shown that the Cox diffusion scheme does not respect either of these properties, which provides an explanation for the necessity to add a nontrivial background horizontal diffusion to that scheme. A new isoneutral diffusion scheme is proposed that aims to satisfy the stated properties and is found to require no horizontal background diffusion.

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