Stability Analysis of Shear Flows

This lecture covers the stability analysis of shear flows, focusing on the Taylor-Goldstein equation and the Brunt-Väisälä frequency. It discusses the conditions for flow instability, the role of stratification, and the implications of varying temperature profiles. The lecture also delves into the dispersion relation, eigenvalue problems, and the distinction between convective and absolute instabilities. Through numerical methods and dimensional analysis, students explore the critical factors influencing flow stability and the transition to different instability types.