Critical-level wave absorption controls chaos in a wave--mean flow system

Wave-mean flow interactions in stratified fluids can drive spontaneous oscillations, yet the mechanisms controlling transitions between periodic and chaotic regimes remain poorly understood. Using a minimal one-dimensional model of wave-driven mean-flow reversals motivated by the quasi-biennial oscillation (QBO), we identify two distinct mechanisms that suppress the formation of multiple extrema in the velocity profile: critical-level momentum deposition by a broad spectrum of undamped small-scale gravity waves, and wave-amplitude growth due to exponential density stratification. Although physically distinct, both mechanisms inhibit the route to chaos and reduce sensitivity to small-scale viscosity, substantially widening the region of periodic behavior in parameter space. These results identify a general internal mechanism for the stabilization of wave-driven oscillations, with direct implications for QBO-like phenomena in geophysical and astrophysical flows.