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The present paper describes a combined experimental and high performance computing study of new specific behaviors of the Strato-Rotational Instability (SRI). The confrontation of low frequency Particle Image Velocimetry (PIV) experimental data with Direct Numerical Simulations reveal new non-linear phenomena and patterns not yet observed in the SRI, that can contribute for our understanding of astrophysical flows, specially regarding phenomena related to accretion disk theories. The experiment designed to investigate these SRI related phenomena consists of a classical Taylor-Couette (TC) system with two concentric cylinders that can rotate independently under stable density stratification due to temperature gradients imposed in the axial direction. In the present investigations, Froude numbers are between 1.5<F<4., and Reynolds numbers vary between 300<Re<1300, while rotation ratio between outer and inner cylinders fixed at 0.35, a value slightly smaller than the Keplerian velocity profile, but beyond the Rayleigh limit. The same experimental configuration is used in the Direct Numerical Simulations investigation, that uses a parallel high-order compact scheme incompressible code that solves the Boussinesq equations. 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.