Nongeostrophic theory of zonally averaged circulation. I - Formulation

A nongeostrophic theory of zonally averaged circulation is formulated using the nonlinear primitive equations (mass conservation, thermodynamics, and zonal momentum) on a sphere. The relationship between the mean meridional circulation and diabatic heating rate is studied. Differences between results of nongeostropic theory and the geostrophic formulation concerning the role of eddy forcing of the diabatic circulation and the nonlinear nearly inviscid limit versus the geostrophic limit are discussed. Consideration is given to the Eliassen-Palm flux divergence, the Eliassen-Palm pseudodivergence, the nonacceleration theorem, and the nonlinear nongeostrophic Taylor relationship.