The zonally averaged circulation in the atmosphere or ocean can be mis
leading if the averaging is performed at constant height. In the ocean
there is apparently anomalously large diapycnal motion forming the so
-called Deacon cell. The atmospheric equivalents are the Ferrel cells.
There are two zonal averaging techniques commonly used to avoid these
spurious cells. One involves averaging at constant density, and this
technique has been used in both fluids. The other technique, which has
so far been applied only in the atmosphere, involves laking into acco
unt perturbation correlation terms to form the residual mean circulati
on. Using a Taylor series expansion, we show that these apparently dis
similar techniques are formally equivalent at leading order in perturb
ation amplitude. The equivalence is demonstrated using output from the
FRAM Southern Ocean numerical model.