A self-consistent numerical model of internal wave-induced mean flow oscillations in polar geometry

The Earth’s Quasi-Biennial Oscillation (QBO) is a natural example of wave-mean flow interaction and corresponds to the alternating directions of winds in the equatorial stratosphere. It is due to internal gravity waves (IGW) generated in the underlying convective troposphere. In stars, a similar situation is predicted to occur, with the interaction of a stably-stratified radiative zone and a convective zone. In this context, we investigate the dynamics of this reversing mean flow by modelling a stably-stratified envelope and a convectively unstable core in polar geometry. Here, the coupling between the two zones is achieved self-consistently, and IGW generated through convection lead to the formation of a reversing azimuthal mean flow in the upper layer. We characterise the mean-flow oscillations by their periods, velocity amplitudes, and regularity. Despite a continuous broad spectrum of IGW, our work show good qualitative agreement with the monochromatic model of Plumb and McEwan (1978). If the latter was originally developed in the context of the Earth’s QBO, our study could prove relevant for its stellar counterpart in massive stars, which host convective cores and radiative envelopes.

💡 Research Summary

The paper presents a self‑consistent two‑dimensional numerical experiment that reproduces the reversal of a mean azimuthal flow driven by internal gravity waves (IGWs) in a configuration that mimics the core‑envelope structure of massive stars. The authors adopt a polar (disk‑like) geometry, representing an equatorial slice of a star, and solve the incompressible Navier‑Stokes equations together with the temperature equation under the Boussinesq approximation. The key novelty is that the convective core (CZ) and the overlying radiative envelope (RZ) are both modelled explicitly; IGWs are generated naturally by turbulent convection rather than being imposed as an external forcing.

A piecewise‑linear equation of state makes the thermal expansion coefficient change sign at a prescribed inversion temperature T_i, thereby creating a stably stratified outer layer (N²>0) and an unstable inner layer (N²<0). The strength of the stratification is controlled by a nondimensional stiffness parameter S, which sets the Brunt‑Väisälä frequency N in the envelope. Internal heating is prescribed as a Gaussian heat source Q(r)=Q₀ exp