Baroclinic instability of an idealized model of the polar night jet

The zonal current u(z), considered by Murray (1960, Section 4), as a model for the polar night jet in the lower stratosphere, has no shear in the model troposphere, and constant vertical shear uz in the stratosphere, u being a continuous function of z. The Richardson number is large. It is shown that this zonal current is always unstable, in the absence of dissipation, to small‐amplitude wave disturbances of essentially the same kind as those found in the theories of Charney and Eady. But, for numerical parameter values appropriate to the base of the polar night jet, predicted growth rates are small, and the disturbances have high zonal wave number (say 5 to 10) and are not very deep (several km at most).