Eliassen-Palm Flux and Eddy Potential Vorticity Flux for a Nonquasigeostrophic Time-Mean Flow

Abstract

Eliassen?Palm theory is formulated for a time-mean flow in an isopycnic coordinate system. An expression is derived for the Eliassen-Palm flux E in this context. In isopycnic coordinates it is natural to approximate the Ertel potential vorticity Q by linearizing about the time mean of layer thickness. This approximation, called ?, is shown to he closer to Q in the absence of the quasigeostrophic assumption than the usual quasigeostrophic potential vorticity q obtained by linearizing about a constant layer thickness. It is also shown that the ?? flux is close to the divergence of E for geostrophic eddies on an f plane: a nonquasigeostrophic analog of the relationship between the q? flux and the divergence of the quasigeostrophic Eliassen-Palm flux. The application of these diagnostic in analyzing eddy-mean flow interactions is illustrated with a five-layer isopycnic ocean model, using a zonal channel with a cyclic buoyancy forcing to capture the broadening and fanning out of the North Atlantic Current.