A theory is presented for the propagation of wave packets in a slightly unstable baroclinic shear flow in a quasi-geostrophic two-layer model on the beta plane. The theory for inviscid motions is considered and packet solutions resembling solitary waves are found. It is shown that the propagation speed of the packet, which is a function of its amplitude, exceeds the most naturally defined group velocity. A physical explanation is presented and it is suggested that the enhancement of the signal velocity above the group velocity is a general property of systems possessing linear instability and nonlinear stability.
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Joseph Pedlosky (1972) studied this question.