A global map of meso-scale eddy diffusivities based on linear stability analysis

Using a hydrographic climatology, global maps of meso-scale eddy kinetic energy (EKE), diffusivities for mixing along isopycnals (isopycnal diffusivity) and for the advective effect of meso-scale eddies (skew diffusivity) are created using properties of the fastest growing unstable baroclinic waves and a simple ad hoc scaling of the amplitudes from linear stability theory. Amplitudes of EKE compare well with near-surface observational estimates based on satellite data and results of an eddy-permitting model, but show a low bias in regions where eddies are not generated locally but propagate into, which will likely transfer both to the diffusivities. In agreement with previous studies we find largest diffusivities in the deep Antarctic Circumpolar Current, and in the shallow western boundary and low latitude westward currents. In agreement with analytical consideration, we find that isopycnal diffusivities are increased at the depth of the steering level where unstable waves and mean flow propagate at the same speed, while skew diffusivities exhibit less vertical dependency, and that isopycnal diffusivities are roughly three times larger than skew diffusivities at the steering level. It is shown that the vertical structure of the diffusivities can be explained to a large extent by the effect of the planetary vorticity gradient which leads to a decrease of skew diffusivities at the surface (bottom) and to a downward (upward) shift of the steering level, and thus the maximum of isopycnal diffusivities, for eastward (westward) flow.