An updated effective diffusivity for the Southern Ocean: evidence of mixing supression by the mean flow and implications for the MOC.

Mixing by mesoscale eddies in the Southern Ocean is crucial for determining large scale ocean circulation. Our understanding is limited by sparse observations and poor resolution of the relevant processes in models. One approach to estimate the mixing by mesoscale eddies is the calculation of a Nakamura effective diffusivity using a tracer advected by velocities from satellite altimetry. We present an updated calculation of the Nakamura effective diffusivity for the Southern Ocean for the period 1993-2014. We show lower mixing in the ACC core than previously estimated, around 500 m$^2$s$^{-1}$ compared to around 900 m$^2$s$^{-1}$ for 1996-2001 based on previous generation altimetry. This drop is associated with the mixing-suppression effects of higher zonal velocities, with time and streamwise mean zonal velocities peaking at around 12 cm s${-1}$ compared with around 9 cm s${-1}$ previously. We show how common mixing parametrisations do not match well with our updated results, highlighting the shortcomings of the assumptions made in the derivation of these parametrisations. The new estimate of mixing can be used to imply the overall strength of the meridional overturning circulation in the Southern Ocean via a stream-wise averaged form of the meridional momentum equation. However, we show that the balance between eddy mixing, Ekman transport and buoyancy forcing is highly seasonally dependent. These results confirm the presence of suppression of eddy mixing by the mean flow in the ACC core, but shows that common parametrisations are not sufficient to represent this accurately. Our work also shows that the stream-wise and time averaged view of meridional momentum balance cannot capture important spatially local and seasonally varying processes.