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Notes on “Subduction of water masses in an eddying ocean” by Marshall (1997)

“Solutions from an idealized two-dimensional ocean model are presented to illustrate the eddy contribution to subduction rates in the Southern Ocean and in an open-ocean convective chimney. In the Southern Ocean, the net subduction rate is the residual of the Eulerian-mean and eddy contributions, which cancel at leading order. [...] In a convective chimney, in contrast, the Eulerian-mean subduction rate is vanishingly small and the subduction is contributed entirely by mesoscale eddies.”

Andrews et al. (1987) describes the difference between the “bolus velocity”, the “residual-mean velocity” and the “Lagrangian-mean velocity”, and the situations when these quantities are equal.

The case of Fig. 8a –adiabatic and without buoyancy forcing– is equivalent to the case of the Lagrangian transport with inviscid conditions and no external PV forcing: in both cases, the Eulerian-mean flow and the eddy-driven (Stokes) flow cancel exactly each other. Question: in the case of Fig. 8b, what allows the water to move meridionally? Is it because there is squeezing of isopycnals at depth and the PV contours are in the SW-NE direction (see “Note the subtle adjustments to the isopycnals to accommodate the additional bolus velocities”)?

I am not sure what is the equivalent of the open-ocean chimney (case with no meridional boundary?).

“On the large-scale, the subduction rate for a water mass is independent of the partitioning of the subduction between mean and eddy components.”

Eq. (A4), which is the parameterization of Gent and McWilliams (1990) is equivalent to the Lagrangian-mean PV equation beta*VL = -r*QL.

Who built on Marshall (1997)?