Williams, G. P., and J. B. Robinson, 1974: Generalized Eady waves with Ekman pumping. Journal of the Atmospheric Sciences, 31 (7), 1768-1776.

Abstract: The effects of Ekman layers on generalized Eady waves (i.e., height-varying static stability and shear) are examined. The non-constancy of N(z) and u _z modify the classical Eady results but do not introduce any new effects. Thus, a short-wave cutoff is always found for flows with double Ekman layers but never for flows with a single Ekman layer.
By comparing the analytical solutions with a numerically simulated annulus wave, we are able to categorize the latter quite accurately.