Bounds on the phase speed and growth rate of barotropic–baroclinic instability problem

We consider the barotropic–baroclinic instability problem for zonal flows on the β-plane satisfying the boundary conditions ∂ U /∂ z = 0 at z = 0, z T . First, we obtain a new estimate for the growth rate of any unstable normal mode. Then, we prove the boundedness of the wave velocity of non-singular neutral modes. Finally, we obtain parabolic instability regions, which improve Pedlosky's instability region for two classes of flows.