Isentropic zonal average formalism and the near‐surface circulation

Abstract

SUMMARYThe isentropic zonal average formalism is extended to include a rigorous treatment of the bottom boundary of the atmosphere. We define a 'surface zone', where isentropes in the latitudinal plane are interrupted by the earth's surface. The zonal average equations of motion and their time average in isentropic coordinates are rederived in the presence of the surface zone. Applying the extended formalism to a baroclinic wave model, we show that near-surface equatorward mean flow is driven by eastward surface form drag in isentropic coordinates, which in turn is related to poleward geostrophic potential temperature flux at the surface. A potential vorticity-potential temperature picture of extratropical general circulation dynamics above and within the surface zone is presented. We highlight the importance of poleward mean flow in the upper region of the surface zone and investigate the antisymmetric distribution of mean meridional mass flow about the median potential temperature of surface air.

The Force Balance of the Southern Ocean Meridional Overturning Circulation

“…Koh and Plumb (2004) suggest to interrupt the zonal averaging in those regions without adjusting the normalization of the averages by still dividing by the full length of the latitude circle and duration of the averaging period, which corresponds to setting h( f 1 z)/h 5 0, where h 5 0. This approach is followed here, and the reader is referred to Schneider (2005) and Jansen and Ferrari (2013, manuscript submitted to J. Atmos.…”

The Southern Ocean meridional overturning circulation as diagnosed from an eddy permitting state estimate

“…This balance has proven appropriate in the "Middleworld" region of the atmosphere where isentropes do not intersect the Earth's surface. In the region where atmospheric isentropes do intersect topography, the surface zone or "Underworld", pressure forcing becomes significant (Koh and Plumb, 2004;Schneider, 2005).…”

“…Recently it has been shown, however, that the meteorologists theories must include the effects of pressure forcing on any isentrope that may intersect horizontal boundaries (Koh and Plumb, 2004;Schneider, 2005). This, of course, is the case for the ocean as well.…”

“…A conflict arises as to what to do when isopycnals, and thus h, vanishes. When this occurs one could either set P * = f , as in Schneider (2005), or P * = 0, as in Koh and Plumb (2004). The advantages of each are discussed in detail in Schneider (2005).…”

“…The advantages of each are discussed in detail in Schneider (2005). For the temporal averaging in this work the convention of Koh and Plumb (2004) was used (convention II as discussed in Schneider (2005)), such that P * = 0 where isopycnals vanish. As zonal integration was carried out on full terms (e.g.…”