Development of a Two-Dimensional Zonally Averaged Statistical-Dynamical Model.Part II: The Role of Eddy Momentum Fluxes in the General Circulation and their Parameterization

Abstract

The effect of eddy momentum fluxes on the general circulation is investigated with the aid of perpetual January simulations with a two-dimensional, zonally averaged model. Sensitivity experiments with this model show that the vertical eddy flux has a negligible effect on the general circulation, while the meridional eddy flux has a substantial effect. The experiments on the effect of the mefidional eddy flux essentially confirm the resultsfound by Schneider in a similar (but not identical) set of sensitivity experiments, and, in addition, show that the vertical structure of the mefidional eddy flux has a relatively small effect on the general circulation. In order to parameterize the vertically integrated mefidional eddy momentum flux, we take Green's parameterization of this quantity and generalize it to allow for the effects of condensation. In order to do this, it is necessary to use Leovy's approximation for the eddy fluctuations in specific humidity. With this approximation the equivalent potential vorticity defined by Saltzman is conserved even when condensation occurs. Leovy's approximation also allows one to generalize the relation between quasi-geostrophic potential vorticity and theEliassen-Palm flux by replacing the potential vorticity and potential temperature by the corresponding equivalent quantities. Thus, the eddy momentum flux can be related to the eddy fluxes of two conserved quantities even when condensation is present. The eddy fluxes of the two conserved quantities are parametefized by mixing-length expressions, with the mixing coefficient taken to be the sum of Branscome's mixing coefficient, plus a correction which allows for nonlinear effects onthe eddy structure and ensures global momentum conservation. The parametefization of the mefidional eddy transport is tested in another perpetual January simulation with the two-dimensional averaged model. The results are compared with a parallel three-dimensional simulation which calculates the eddy transport explicitly. The parameterization reproduces the latitudinal and seasonal (interhemisphefic) variations and the magnitude of the eddy transport calculated in the three-dimensional simulation reasonably well.