Nongeostrophic Theory of Zonally Averaged Circulation. Part I: Formulation

Abstract

A nongeostrophic theory of zonally averaged circulation is formulated using the nonlinear primitive equations on a sphere, taking advantage of the more direct relationship between the mean meridional circulation and diabatic heating rate which is available in isentropic coordinates. Possible differences between results of nongeostrophic theory and the commonly used geostrophic formulation are discussed concerning (i) the role of eddy forcing of the diabatic circulation, and (ii) the ?nonlinear nearly inviscid? limit versus the geostrophic limit. A set of general diagnostic tools comparable in scope to their geostrophic counterparts is given in Part I, including (i) a generalized definition of Eliassen?Palm flux divergence (without restriction to small amplitudes, to steady state or to adiabatic flows), the vanishing of which is a necessary condition for nonacceleration, (ii) a generalized nonlinear Taylor formula that relates the flux of Ertel's potential vorticity to the Eliassen?Palm flux divergence and (iii) a relationship between the Eliassen?Palm flux divergence and isentropic mixing coefficient, Kyy, used in chemical tracer transport equations in isentropic coordinates. From the mean momentum budget, we give in Part II in estimate of the Eliassen?Palm flux divergence using fitted ?observed? field of net radiative heating rate. From this an estimate of the magnitude and latitudinal/seasonal variation of Kyy is also provided.