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It is shown that the effects of mesoscale eddies on tracer transports can be parameterized in a large-scale model by additional advection and diffusion of tracers. Thus, tracers are advected by the effective transport velocity, which is the sum of the large-scale velocity and the eddy-induced transport velocity. The density and continuity equations are the familiar equations for adiabatic, Boussinesq, and incompressible flow with the effective transport velocity replacing the large-scale velocity. One of the main points of this paper is to show how simple the parameterization of Gent and McWilliams appears when interpreted in terms of the effective transport velocity. This was not done in their original 1990 paper. It is also shown that, with the Gent and McWilliams parameterization, potential vorticity in the planetary geostrophic model satisfies an equation close to that for tracers. The analogy of this parameterization with vertical mixing of momentum is then described. The effect of the Gent and McWilliams parameterization is illustrated by applying it to a strong, sloping two-dimensional front. The final state is that the front is flat, corresponding to a state of minimum potential energy. However, the amount of water of a given density has not been changed and there has been no flow across isopycnals. These properties are not preserved with horizontal diffusion of tracer. Finally, the Levitus dataset is used to estimate the effects of the Gent and McWilliams parameterization. The zonal mean meridional overturning streamfunction for the eddy-induced transport velocity has a maximum of 18 Sverdrups near the Antarctic Circumpolar Current. The associated poleward heat transport is 0.4 petawatts. The maximum poleward heat transport in the Northern Hemisphere is 0.15 petawatts at 40°N. These values are the same order of magnitude as estimates from observations and regional eddy-resolving ocean models.
Gent et al. (Sat,) studied this question.