Critical layer instability in baroclinic flows

Abstract It is shown that for all inviscid, adiabatic, quasi‐geostrophic motions in a Boussinesq liquid or in a compressible atmosphere, subject to the usual boundary conditions, the integral over the fluid of the northward eddy flux of potential vorticity vanishes, provided a generalized interpretation of potential vorticity is adopted near rigid horizontal boundaries. For an infinitesimal disturbance in a normal mode to a general zonal flow, the presence of a critical layer within the fluid excludes the existence of stable modes, except in exceptional circumstances. A stable, or slowly growing mode, is associated with a down‐gradient flux of potential vorticity near the critical layer, which does not vanish as the growth rate tends to zero, and can only be balanced by the general growth in the disturbance.