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Previous comparisons of experimental data with nonlinear numerical simulations of density stratified Taylor–Couette (TC) flows revealed nonlinear interactions of strato-rotational instability (SRI) modes that lead to periodic changes in the SRI spirals and their axial propagation. These pattern changes are associated with low-frequency velocity modulations that are related to the dynamics of two competing spiral wave modes propagating in opposite directions. In the present paper, a parameter study of the SRI is performed using direct numerical simulations to evaluate the influence of the Reynolds numbers, the stratification, and of the container geometry on these SRI low-frequency modulations and spiral pattern changes. The results of this parameter study show that the modulations can be considered as a secondary instability that are not observed for all SRI unstable regimes. The findings are of interest when the TC model is related to star formation processes in accretion discs. This article is part of the theme issue ‘Taylor–Couette and related flows on the centennial of Taylor’s seminal Philosophical Transactions paper (part 2)’.

<p>Using high-order discretization on a High-Performance Computing framework, direct numerical simulations of a differentially heated rotating annulus are performed. The geometry of the baroclinic wave tank is similar to the new atmospheric-like experiment designed at BTU Cottbus-Senftenberg (Rodda et al., 2020), which also consists of a differentially heated rotating annulus. The experimental observations reveal  spontaneous emissions of inertial-gravity waves in the baroclinic wave jet front in accordance with Hien et al. (2018). The different length scales of inertial-gravity instabilities and the baroclinic waves make direct numerical simulation challenging. This motivates the current design of a new higher-order/HPC solver devoted to stratified rotating flows (Abide et al., 2018). Specifically, some features of compact scheme discretizations are used to combine efficiently parallel computing and accuracy for reducing DNS wall times. The ability to reproduce experimentally measured flow regimes with non-axisymmetric regular steady waves to the vacillation regimes is also discussed.</p><p>S. Abide et al. (2018), Comput Fluids 174:300-310.<br>S. Hien et al. (2018), J Fluid Mech 838:5–41.<br>C. Rodda et al. (2020), Exp Fluids 61:2.</p>