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08.14.2013: Notes on Abernathey et al. (2013) “Diagnostics of Isopycnal Mixing in a Circumpolar Channel”

Abernathey et al. (2013) compare different methods to estimate the diffusivity in a simple model of the Antarctic Circumpolar Current and show that these estimates are equivalent and, most importantly, are also equivalent to estimates obtained from observations (=”imperfect” dataset). One of these methods is the technique of Plumb and Mahlman (1987), which has also been applied to the ocean by Bachman and Fox-Kemper (2013). A possibly important result is the fact that the “thickness diffusivity” of Gent and McWilliams (1996) does not resemble (in amplitude or spatial structure) to the diffusivity obtained from either a family of passive tracers (the Plumb and Mahlman 1987’s technique), Nakamura’s “effective diffusivity” averaged along isopycnal surfaces or the diffusivity of either quasi-geostrophic or Ertel potential vorticity.

Several comments I would like to make. First, their net meridional transport arises solely because of the presence of a sponge layer along the northern boundary, so that you are not going to learn anything about the processes that impose the meridional transport. Second, they neglect the model subgrid mixing because they say it is important only in the tracer variance equation, not in the mean tracer equation, for flows with large Peclet number; I would have liked a reference that demonstrates this point. Third, how does the result change when the amplitude of the forcing within the sponge layer is changed; eddies are generated, after all, because of the instability of the zonal flow which is itself imposed by the forcing so we might see a change in eddy diffusivity when the forcing changes.

Question: They mention the issue of the parameterization of the eddy buoyancy diffusivity. But what about the parameterization of the eddy PV diffusivity, which involves the diffusivity in the momentum equations as well? Should we not parameterize these as well?

I like this paper because it shows the link between different methods to compute the diffusivity. I am glad they have applied the technique of Plumb and Mahlman (1987) – which I think is the ultimate one when working with a model. I am still interested to see how important is the horizontal Stokes drift (Stokes drift arising from horizontal velocity correlation); I suspect (hope) that this component may be important wherever there is large horizontal velocity divergence, such as along the Gulf Stream and Kuroshio Extension. To study these, I could compute the Lagrangian mean flow, the bolus velocity and the Eulerian mean and see the differences between them. If the Stokes drift is not just the bolus velocity then this would need to be parameterized as well.