An Idealized Two-Dimensional Atmospheric Model of the Quasi-Biennial Oscillation and Wave-Mean Flow Interactions in the Equatorial Channel

The quasi-biennial oscillation (QBO) is a fundamental mode of atmospheric variability and a textbook example of wave-mean flow interactions. While its general theory has been established about 50 years ago by the seminal works of Holton, Lindzen and Plumb (HLP), it remains an unsettled problem of geophysical fluid dynamics and a challenge for atmospheric general circulation models (GCM). In this study, we investigate wave-mean flow interaction and QBO-like dynamics in a new idealized 2D (altitude-longitude) numerical setup based on the Weather Research and Forecasting (WRF) model. The model is designed to reproduce in 2D the minimal 1D model proposed by HLP. Namely, two gravity waves of opposite phase speed are explicitly resolved; they are forced through periodic heating in the lower part of the domain, and propagate vertically and dissipate through Newtonian cooling and viscous damping. In this configuration, we obtain a periodic wind reversal similar to the QBO. We characterize the evolution of the wave field and momentum budget of the mean flow in both our 2D and the 1D HLP framework. Then, the sensitivity of the flow to model parameters is assessed and compared with theoretical predictions as well as the original HLP model. This exercise highlights the impact of explicit wave forcing on wave-mean flow interactions as well as the role of forcing amplitude and vertical viscosity in shaping the flow. Implications for QBO representations and predictions in a model hierarchy ranging from simple models to GCMs are discussed.