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 and it has been suggested that this is due to rotational components that do not influence the heat budget. We diagnose the rotational component of the horizontal eddy heat flux, as measured by its curl, 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 accounts for more than 95% of the total flux, increasing to more than 99% with increasing lengthscale. Hence, rotational components are still dominant when eddy fluxes are averaged over scales larger than the eddy scales. The rotational component, approximated by that part that is along temperature variance contours, only accounts for a fraction of the total rotational component as measured by the curl, 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. The coherence for the divergence is low since it is associated with very small and noisy features no matter how large the averaging lengthscale. Diffusivities estimated from the eddy heat flux show a high wavenumber dependence and are as high as 10000 ms, reflecting the presence of the rotational component. Using the divergence, more realistic, less wavenumber dependent values are estimated, ranging from 500 ms within the ACC to 3000 ms in the near surface ocean in the Aghulas Retroflection region.