Wave–Mean Flow Interactions and QBO-Like Modulations in Strato-Rotational Instabilities

The Strato-Rotational Instability (SRI) is a hydrodynamic instability, proposed as a possible mechanism for angular-momentum transport in stratified astrophysical accretion disks. It is also a laboratory analogue for rotating stratified shear flows relevant to geophysical and planetary systems, such as  atmospheric dynamics. In Taylor–Couette flows with stable density stratification in the axial direction, the SRI generates spiral patterns that propagate alternately upward and downward along the rotation axis. While such axial reversals have been observed in experiments and numerical simulations in [1, 2], their physical origin and connection to mean-flow dynamics remain to be investigated. Here, we combine numerical simulations consistent with laboratory measurements and reduced (toy) models to investigate the mechanisms driving axial spiral propagation and low-frequency modulation in SRI. Using a Radon Transform decomposition, we isolate upward- and downward-traveling spiral components and show that each exhibits a distinct, slowly varying amplitude modulation. These modulations are phase-shifted and interact through the mean flow, leading to transitions in the direction of the axial spiral propagation. The changes also lead to changes in the axial mean flow velocity. Motivated by these observations, we introduce a reduced toy model consisting of two counter-propagating, modulated wave-like spirals. Despite its simplicity, the model clearly reproduces the observed pattern transitions, demonstrating that linear superposition of individually modulated spirals is sufficient to explain the dynamics. To interpret the simultaneous occurrence of low-frequency spiral and axial mean flow modulations, we propose a quasi-biennial oscillation (QBO)–like mechanism, inspired by several dynamical similarities of the SRI reversals with the atmospheric QBO, where the wave–mean flow interactions drive periodic reversals of the zonal flow [3, 4]. Adapting this framework to rotating stratified shear flows, we derive a reduced inertial-wave model for the axial mean flow. The model predicts periodic reversals and amplitude modulation consistent with SRI observations. Our results suggest that SRI spiral reversals arise from a weak nonlinear coupling between counter-propagating inertial waves and the mean flow, providing an interpretation linking laboratory SRI to the geophysical wave–mean flow interactions.

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