Isopycnal averaging and the residual mean circulation

Abstract

The zonally averaged circulation in the atmosphere or ocean can be misleading 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 taking into account perturbation correlation terms to form the residual mean circulation. Using a Taylor series expansion, we show that these apparently dissimilar techniques are formally equivalent at leading order in perturbation amplitude. The equivalence is demonstrated using output from the FRAM Southern Ocean numerical model.