A new look at equatorial quasi-biennial oscillation models

Abstract

Simplified quasi-biennial oscillation (QBO) models are investigated in light of bifurcation theory. If the two components of the wave forcing are symmetric (ie 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 of Hopf bifurcation takes place; periodic solutions appear that are not symmetric with respect to time. -from Authors