To gain a better understanding of the general circulation in our atmos
phere and of many other geophysical fluid dynamics phenomena, a stabil
ity analysis of strongly nonlinear baroclinic flow in a rotating annul
us has been performed. A dynamic model of baroclinic waves with single
or wave-wave interactions is developed using an Eady-type basic state
modified by two Ekman layers of different strengths. The mathematical
model is developed in terms of the nondimensional stream function and
is solved using a truncated spectral expansion. The expansion coeffic
ients are computed from a set of evolution equations. The influences o
f the imposed temperature contrast, the Ekman layer dissipation, and t
he rotation rate on the main characteristics of the flow have been exp
lored by solving the evolution equations for sequences of Ekman dissip
ation rate, delta, and Stratification parameter, S. The current model
not only produced the regimes observed in the annulus experiments: axi
symmetric zonal flow, steady waves, and amplitude vacillation, but als
o predicted the phenomena of wave number transition.