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A theory is presented for the finite-amplitude behavior of unstable baroclinic waves in a quasi-geostrophic two-layer model. It is shown that in the absence of dissipation the equilibrated finite-amplitude state exhibits an oscillation, both of the mean flow and the baroclinic wave. On the other hand, if sufficient dissipation is present, the final state is a wave whose amplitude is steady and the approach to that state is non-oscillatory.
Joseph Pedlosky (Thu,) studied this question.