Flow instabilities and laminar-to-turbulence transition are ubiquitous with significant importance in the fields of physical sciences and engineering. Those complex flow processes are still not fully understood especially when additional effects are involved ; for instance, fluid stratification, rotation, compressibility, etc. In this seminar, I will talk about two separate subjects : one is about instabilities and transition of shear flows in the presence of both a stable stratification and rotation, and the other is about high-speed compressible boundary-layer instability and its sensitivity to base-state distortion. In the first part, I will discuss two types of instabilities of the stratified Taylor-Couette flow, centrifugal and strato-rotational instabilities. I will present theoretical, experimental and numerical results about these instabilities and transition-to-turbulence to explain the physical mechanisms of the instabilities and demonstrate actual nonlinear phenomena. In the second part, I will show recent results on the sensitivity analysis for the compressible boundary-layer instability that can be further developed as the optimal flow-control tool. I will discuss Mach-number effects on boundary-layer instabilities and how they are sensibly modified when the base flow is disturbed.
