Forced Planetary Waves in a Two-Level Model and Evaluation of the Upper Boundary Condition

Stationary planetary waves forced by orography and diabatic beating are studied using a quasi-geostrophic two-level model on a beta-plane. This study extends a previous one by Trenberth to include the effects of a baroclinic atmosphere with zonal mean wind shear. With the introduction of vertical shear, the temperature field is no longer locked onto the heating field and can become orthogonal so that even though the wave is thermally forced there may not be any generation or loss of energy by diabatic heating. The presence of both thermal and orographic forcing together violates the conditions of nonacceleration of the zonal mean flow. The induced changes in the zonal mean flow strongly depend upon the relative phase of the thermal and orographic forcing. With a specified diabatic heating field, the eddy fluxes and changes of zonal mean flow are not sensitive to the strength of the mean zonal wind shear. By increasing the wind shear, however, the vertically propagating waves become trapped. The trapped waves accelerate the zonal mean flow through an induced meridional circulation distinct from that of the propagating waves. The characteristics of the forced waves can be explained by the local index of refraction. Results indicating important differences between the stationary planetary waves in the two hemispheres are 1) the higher total wave number in the Southern Hemisphere, which arises from the shorter meridional scale, so that the waves are trapped, and 2) interaction between thermal and orographic waves in the Northern Hemisphere which is less likely in the Southern Hemisphere. The limitations of the two-level model with the traditional fixed upper boundary condition, ω = 0 at p = 0, in reproducing forced planetary waves is evaluated by testing the sensitivity of results to a modified radiation upper boundary condition. Distinct differences are found when the planetary waves can propagate vertically. Not only is the response of the planetary waves different in phase and magnitude but also the induced acceleration of the zonal mean flow can be completely opposite. Nevertheless, there is reasonable agreement when the planetary waves are trapped vertically so that the upper boundary conditions have minor impact.