A numerical study of global axisymmetric states and their stability to quasi-geostrophic disturbances

A steady, axisymmetric model of the general circulation is developed as a basis for climate stability studies. The model includes the effects of heating, rotation, and internal friction, but neglects topography. It is assumed that the axisymmetric flow may be modeled by making the Boussinesq and deep convection approximations. The hydrostatic assumption is not made, thus permitting the advective terms to be included in the vertical equation of motion. The initial set of five primitive equations is reduced to three equations in terms of the zonal velocity, meridional streamfunction, and the potential temperature perturbation. The application of the Boussinesq, deep convection, and quasi-geostrophic assumptions limits the ranges of the heating and rotation rates. For values not too far from typical atmospheric values, the model produces a stability boundary separating Hadley from Rossby flow. The boundary is characterized by a particular value of vertical wind shear, which suggests that baroclinic instability is the primary mechanism for the loss of stability. The initial growth rates are largest for longitudinal waves 4-7, also in agreement with studies of baroclinic instability.