Variability of mean-flow reversals in stably stratified fluids with stochastic wave forcing

The quasi-biennial oscillation (QBO) of Earth’s stratosphere is a slowly reversing, large-scale mean flow that is generated by fast, small-scale waves. The variability of QBO reversals in recent years has triggered significant interests in the intrinsic variability of wave-driven mean flows. In this paper, we show a direct connection between the statistical properties of gravity waves randomly emitted at the bottom of a stably stratified fluid and the statistics of mean-flow reversals. We perform wave-resolved, direct numerical simulations of the two-dimensional Navier–Stokes equations under the Boussinesq approximation. We generate waves monochromatic in space at the bottom of the layer using three different types of temporal forcing: a constant-amplitude monochromatic forcing, a finite band polychromatic forcing and a stochastic forcing. We show that the stochastic forcing scheme consistently generates a mean flow with variable reversals and investigate the dependence of the reversal statistics on the wave Reynolds number and forcing correlation time. In particular, we demonstrate that the mean-flow reversals become increasingly variable as the forcing correlation time approaches the characteristic time scale of the reversals. The monochromatic and polychromatic forcing schemes trigger QBO-type flows that are highly regular for most values of the control parameters considered. Thus, the mean-flow variability under stochastic forcing is not linked to secondary mean-flow instabilities in our simulations, but rather evidence that small-amplitude waves can alter large-scale oscillations when their generation is chaotic. Finally, we demonstrate that the first-order statistics of the mean flow are relatively insensitive to the forcing type.