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.