Centrifugal Instabilities: Mechanism and Analysis

This lecture delves into the mechanism and analysis of centrifugal instabilities, focusing on the Rayleigh criterion as a necessary and sufficient condition for stability. The instructor explains the instability analysis process, including the physical mechanism, equations, base state, linearized equations, normal mode expansion, and dispersion relation. The lecture also covers the comparison between theoretical and experimental results, wall-bounded flows, the backward facing step phenomenon, and global dispersion relations. Through the slides, the instructor illustrates the conditions for stability and instability, providing insights into the behavior of fluid flows in different configurations.