Implementing diffusivities from linear stability analysis in a three-dimensional general circulation ocean model

Linear stability analysis is used to predict the vertical and lateral structure for the diffusivity related to meso-scale eddy buoyancy and potential vorticity fluxes in three-dimensional primitive equation models, following a suggestion by Peter D. Killworth. Using two idealized numerical models as example, it is shown that the linear stability analysis yields a consistent lateral and vertical structure for both lateral diffusivities. Parameterizations based on isopycnal thickness or potential vorticity diffusion are shown to be equivalent for constant diffusivities in quasi-geostrophic approximation. For spatially varying diffusivities they yield similar results in the model experiments, although the corresponding diffusivities show different vertical structure.

► Parameterizations of meso-scale eddy effects by isopycnal thickness and potential vorticity mixing are compared.
► Linear instability theory is used to predict the lateral diffusivity for eddy buoyancy fluxes and eddy potential vorticity fluxes.
► The closure is implemented and tested in a three-dimensional primitive equation model.