The Hadley and Rossby regimes in a spherical atmosphere

The properties of the steady Hadley and Rossby regimes for a thermally forced rotating fluid on a sphere are studied. The two layer modified geostrophic model is employed which allows for thermal advection by the divergent wind and time dependent static stability. Heating processes are parameterized using the Newtonian approximation and Rayleigh friction is accounted for. The equations are transformed to spectral form using spherical harmonics and then truncated retaining a simple axisymmetric state and initial, one wave. A time independent Hadley circulation is obtained which is neutral to axisymmetric disturbances but unstable to wave like perturbations for intermediate values of the meridional temperature gradient, indicating the existence of both an upper and lower symmetric Hadley regime. An analytical solution for the steady Rossby circulation is determined for values of the meridional temperature gradient where the Hadley regime is unstable. Linear perturbation theory is used to show that within the steady Rossby regime two or more waves cannot exist simultaneously.