Held, I. M., R. L. Panetta, and R. T. Pierrehumbert, 1985: Stationary external Rossby waves in vertical shear. Journal of the Atmospheric Sciences, 42 (9), 865-883.

Abstract: The structure of stationary Rossby waves in the presence of a mean westerly zonal flow with vertical shear is examined. There is typically only one stationary vertical mode, the external mode, trapped within the troposphere. For more that one tropospheric mode to exist, we find that vertical shears must be smaller than those usually observed in extratropical latitudes. The vertical structure, horizontal wavenumber and group velocity of the external mode, and the projection onto this mode of topographic and thermal forcing are studied with continuous models (a linear shear profile as well as more realistic basic states), and a finite-differenced model with resolution and upper boundary condition similar to that used in GCMs. We point out that the rigid-lid upper boundary condition need not create artificial stationary resonances, as the artificial stationary vertical modes that are created are often horizontally evanescent.
The results are presented in a form which allows one to design the equivalent barotropic model that captures the external mode's contribution to the stationary wave field. It is found, in particular, that the wind blowing over the topography in such a barotropic model should generally be larger than the surface wind but smaller than the wind at the equivalent barotropic level. Also, the group velocity of the stationary external mode in realistic vertical shear is found to be considerably greater than that of the stationary Rossby wave in the equivalent barotropic model.