Baroclinic instability and the short wavelength cut‐off in terms of potential vorticity

Abstract The stability is discussed of an infinitesimal quasi‐geostrophic perturbation to a baroclinic zonal wind which is independent of latitude, in terms of a two‐layer inviscid model with parallel but sloping upper and lower boundaries, so that the northwards gradient of potential vorticity in each layer is equal and opposite, but not a simple multiple of the difference between the basic eastward velocities. A long wavelength cut‐off to the instability is possible, as well as a short wavelength cut‐off. The mechanism for the instability is described qualitatively in terms of the balance between east‐west advection of perturbation potential vorticity, and generation by north‐south motions in the basic gradient, and the reasons for both cut‐offs are clarified. The short wavelength stable modes are described as advected Rossby waves in either the upper or the lower layer. This qualitative description is then extended to apply to the short wavelength cut‐off found by Eady, and to the short wavelength Eady modes, which are always de‐stabilized by a small gradient of potential vorticity in the interior of the fluid, together with the action of a critical layer.