J. Atmos. Sci. (1998), 55, 3024-3041.
The paper investigates axially symmetric stationary balanced flow of a stably stratified dry non-Boussinesq atmosphere on the f-plane. The circulation is forced in the troposphere through thermal relaxation towards a specified equilibrium temperature and is damped through Rayleigh friction in the interior of the domain. Surface friction maintains weak surface winds. Like in the analogous zonally symmetric problem studied by Plumb and Hou (1992) there is threshold behaviour in the frictionless limit with a thermal equilibrium (TE) solution for subcritical forcing and a highly nonlinear so-called angular momentum conserving (AMC) solution for supercritical forcing. The latter is characterized by a sharp outward edge of the vortex circulation and a non-vanishing secondary cross-vortex circulation. In the frictionless limit, the secondary circulation does not reach above the region of the thermal forcing. Noticeable differences of the current problem with respect to the zonally symmetric problem arise from the strong non-linearity of the thermal wind equation and the nonzero thermal forcing right on the axis of symmetry. For the highly nonlinear AMC solution an approximate analytical theory is presented and verified by use of a numerical Eliassen balanced vortex model. The latter is also used to investigate the non-linear dependence of the secondary circulation on the Rayleigh friction coefficient and the penetration of the secondary circulation above the tropopause. An analytic Green's function solution for the linearized problem gives insight into nonlinear asymptotic dependences. Thinking in terms of an Eliassen balanced vortex model offers a new view on the secondary circulation in the AMC regime.