On non-linear baroclinic adjustment with the stratosphere

The effect of the stratosphere on the baroclinic adjustment of a nonlinear Eady model is presented. The classical linear Eady model has been modified by including an additional layer (the stratosphere), Ekman dissipation at the bottom boundary and a Newtonian cooling at the surface and the tropopause, respectively; non-linearity is introduced by wave-mean flow interaction for a single eddy mode. Results for the rigid-lid case and for small troposphere/stratosphere stratification ratio are compared with those for the linear Eady model with Ekman dissipation at the surface. For these cases model solutions consist of a steady zonal correction and an eddy field with a travelling constant amplitude wave. The equilibrated field, as a function of small stratification ratio, shows that the minimum amplitude of the eddy component raises to a height close to the tropopause (its steering level), denoting that the wave solution becomes vertical evanescent. When realistic values for the static stability in the stratosphere are considered, the zonal correction is no more time independent and reveals a degree of chaotic behaviour, while the eddy field is fully chaotic. Effects of changes in the zonal wind vertical shear and a further decreasing static stability in the stratosphere are also analysed. Results suggest that the minimum amplitude is, in average, higher than the one computed for the classical rigid lid with Ekman dissipation at the surface. Thus, as in the linear Eady model, the stratosphere induces a stabilising effect on the baroclinic dynamics. Finally, the model solutions are compared with the time behaviour of a simplified General Circulation Model