Experiments and long-term high-performance computations on amplitude modulations of strato-rotational flows

Abstract

The present paper describes a combined experimental and high-performance computing study of new specific behaviours of the Strato-Rotational Instability (SRI). The SRI is a purely hydrodynamical instability that consists of a classical Taylor–Couette (TC) system under stable axial density stratification. The density stratification causes a change on the marginal instability transition when compared to classical non-stratified TC systems, making the flow unstable in regions where – without stratification – it would be stable. This characteristic makes the SRI a relevant phenomenon in planetary and astrophysical applications, particularly in accretion disk theory. In spite of many advances in the understanding of strato-rotational flows, the confrontation of experimental data with non-linear numerical simulations remains relevant, since involved linear aspects and non-linear interactions of SRI modes still need to be better understood. These comparisons also reveal new non-linear phenomena and patterns not yet observed in the SRI that can contribute for our understanding of geophysical flows. The experiment designed to investigate these SRI-related phenomena consists of two cylinders that can rotate independently, with the space between these two vertical cylinders filled with a silicon oil. For obtaining a stable density stratification along the cylinder axis, the bottom lid of the setup is cooled, and its top part is heated, with temperature differences varying between , establishing an axial linear gradient, leading to Froude numbers between 1.5<Fr<4.5, where is the inner cylinder rotation and N is the buoyancy frequency. The flow field resulting from the cylinders rotation interacting with the stable density stratification is measured using low frequency Particle Image Velocimetry (PIV). In the present investigation, we focus on cases of moderate Reynolds numbers (, based on the inner cylinder radius and angular velocities), varying between and , and rotation ratio between outer and inner cylinders fixed at , a value slightly smaller than the Keplerian velocity profile, but beyond the Rayleigh limit. The same experimental configuration is also investigated by performing several Direct Numerical Simulations using a parallel high-order compact schemes incompressible code that solves the Boussinesq equations combining a 2d-pencil decomposition and the reduced Parallel Diagonal Dominant for an efficient parallelization. Both simulations and experiments reveal, in agreement with recent linear stability analyses, the occurrence of a return to stable flows with respect to the SRI when the Reynolds numbers increase. Low frequency velocity amplitude modulations related to two competing spiral wave modes, not yet reported, are observed both numerically and experimentally.