Lee, S-Y., and I. M. Held, 1991: Subcritical instability and hysteresis in a two-layer model. Journal of the Atmospheric Sciences, 48(8), 1071-1077.

Abstract: A two-layer quasi-geostrophic model forced by surface friction and radiative relaxation to a jetlike wind profile can exist in either a wave-free state or in a finite-amplitude wave state, over a substantial region of the model's parameter space. The friction on the lower layer must be much stronger than the thermal relaxation, and the upper layer must be nearly inviscid, for this behavior to be observed. Consistent with this behavior, weakly unstable waves are found that do not stabilize the flow; instead, their growth rate increases with wave amplitude. We attempt to provide a physical explanation for this behavior in terms of 1) the competition between the stabilizing effect of the lower-layer potential vorticity fluxes and the destabilizing effect of nonlinear critical layer formation associated with the upper-layer fluxes, and 2) the tendency of surface drag to restore the vertical shear at the center of the jet by damping the surface westerlies generated by the baroclinic instability.