Abstract
Simplified quasi-biennial oscillation (QBO) models are investigated in light of bifurcation theory. If the two components of the wave forcing are symmetric (i.e., it is a standing wave), the model has a trivial steady solution of no mean zonal flow. The steady solution becomes unstable with respect to an oscillatory eigenmode when the amplitude of the wave forcing exceeds a critical value. Periodic solutions branch off at that point from the steady solution as a result of a Hopf bifurcation. The periodic solutions are well known QBO-type solutions.
If the two components are not symmetric as in the case of a Kelvin wave and a Rossby-gravity wave, the model has a nontrivial steady solution with nonzero mean zonal flow. As in the symmetric case a Hopf bifurcation takes place; periodic solutions appear that are not symmetric with respect to time.
A two-level, prototype model is developed to analyze the QBO mechanism analytically and to get dynamical insights easily. Both vertical diffusion and the shielding effect, which is an integrated effect of wave-momentum flux absorption below a given level, are necessary to obtain periodic solutions (Hopf bifurcations).
