Transitions from Hadley to Rossby Flows in Internally Forced Rotating Spherical Systems

Abstract

The possibility of global-scale transitions between atmospheric Hadley and Rossby regimes is investigated with a highly idealized, nonlinear, vertically continuous, rotating, spherical system. Low-order spectral versions of the model are used both to calculate ideal Hadley states and to determine their stabilities to certain three-dimensional baroclinic disturbances of any zonal wavenumber. The flow is forced by an idealized axisymmetric heating pattern based on zonally averaged atmospheric data, and is dissipated using an eddy viscosity formulation. The dominant modes in the heating pattern force a single meridional cell between the equator and the poles that is compatible with the simple boundary conditions. As the heating rate is increased, these states exchange stability with temporally periodic solutions that have the characteristics of Rossby waves. Although Ekman boundary layer and cumulus friction effects are not included, the transports of heat and momentum by the zonally averaged Rossby flow are reasonable. When all combinations of heating and rotation rates are used, a transition curve separating the ideal Hadley and Rossby regimes is found. The critical values of the heating rates are made more realistic through the use of an effective eddy viscosity that represents energy transports arising from the products of the sub-Hadley and sub-Rossby scale perturbations. It is shown that a transition from Hadley flow to wavenumber 5 Rossby flow is preferred. This result, which agrees with standard baroclinic instability results, gives a reasonable Rossby wave bifurcation from the Hadley solution. For the cases examined, it is found that the upper symmetric Hadley regime does not exist and that the Hadley to Rossby transition depends on the values of the eddy viscosities. Indeed, the dependence of the preferred zonal wavenumber on the values of the eddy viscosities suggests that small changes in the values of these parameters might result in large changes in the Rossby regime.