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Notes on estimating eddy fluxes of tracers

Only the divergent part of eddy fluxes matters in the tracer budget but decomposing the eddy flux into its divergent and rotational part is difficult and probably impossible as the accuracy needed in the numerical calculation is still not enough: see section 6 of Griesel et al. (2009). Griesel et al. (2009) found also that the rotational component dominates at all scales so no amount of (zonal) averaging exists that could isolate the divergent component; one exception might be in the Southern Ocean where the total zonal integral of the rotational component cancels in theory.

To bypass the above problem, one can consider only the divergence of the flux without knowing the actual divergent component of the flux.

Another problem seems to be in the definition of the eddy component of the eddy advective flux. To define this component, one need to define the mean flow; Lee et al. (2007) defines the mean flow from the “vertical” derivative in isopycnal space of the streamfunction, itself deduced from the time-mean flow at z levels. Nishikawa et al. (2010), however, simply defines the mean flow as the time-mean flow at z levels re-mapped onto isopycnal levels; in their case, the eddy velocity is simply the bolus velocity. Notice a third definition of the mean flow exists: the mean flow averaged in time along isopycnal. This definition is the one used to define the bolus velocity. It is the latest that seems to be used in Lee and Williams (2003).