Abstract
The stability of a small but finite amplitude stationary baroclinic ultra‐long wave associated with a constant zonal flow is considered. A trapped primary is found to be stable, but a propagating primary can be unstable with minimum e‐folding times of two to four days for wavenumbers one and two. The amplifying disturbance is constrained to have the same north‐south structure as the primary. It consists of a wave with the same east‐west wavenumber as the primary and a zonal mean component. It is shown to grow directly at the expense of the primary by resonantly interacting with it. The wave component of the amplifying disturbance has a very large vertical wavelength such that it is almost barotropic. It propagates with a phase speed that is close to the basic westerly wind speed. The zonal mean disturbance component decays rather rapidly with height.
The theoretical growth rates are found to compare favourably with those of growing ultra‐long waves at lower stratospheric levels during November 1970.
A crucial assumption in the analysis concerns the nature of the singular region for the potential vorticity equation at large enough heights. The region is assumed to be totally absorbing to upward‐moving wave energy.