Assessing eddy heat flux and its parameterization: A wavenumber perspective from a 1/10° ocean simulation

Diffusivities diagnosed from eddy heat fluxes in eddying models tend to show unphysically large positive and negative values. These have been attributed to rotational components that do not influence the heat budget. The rotational component of the horizontal eddy heat flux is diagnosed in the Southern Ocean of the 1/10° Parallel Ocean Program as a function of averaging lengthscale. At the scales at which most of the eddy heat flux energy occurs, the rotational component, as measured by its curl, accounts for more than 95% of the total flux, increasing to more than 99% with increasing lengthscale. Hence, rotational components are the dominant component of eddy fluxes even when they are averaged over scales larger than the eddy scales. The rotational component can be approximated by its projection along temperature variance contours; however this only accounts for a fraction of the total rotational component, leaving a residual that is still more rotational than divergent.The eddy heat flux can be parameterized as a function of averaging lengthscale using coherence analysis. The meridional eddy heat flux is most coherent with its parameterizations on lengthscales larger than 50°, but this coherence is due to the rotational component. The divergence of the eddy heat flux is most coherent with the divergence of the parameterizations on scales less than 4°, where the curl of the eddy heat flux has a minimum.Diffusivities estimated from the eddy heat flux show a high wavenumber dependence and are as high as 15,000m2s-1, reflecting the presence of the rotational component. Using the divergence, more realistic, less wavenumber dependent values are estimated, ranging from 500m2s-1 within the ACC to 1000m2s-1 in the near surface ocean in the Agulhas Retroflection region.