Hydrodynamic Instabilities: A Theoretical Overview

This lecture covers various types of flow instabilities, including Vortex shedding, Saffman-Taylor, Flow separation, Tollmien-Schlichting, Rayleigh-Taylor, Lift-up and Streaks, Traffic waves, Meandering instability, Gravito-capillary waves, Taylor-Couette, Rayleigh-Plateau, Tearing instability, Rayleigh-Benard, Coiling instability, Benard-Marangoni Kelvin-Helmholtz. It discusses the historical context of hydrodynamic linear instability theory, the physical mechanisms behind surface tension, and the analysis of instability through equations, boundary conditions, and normal mode expansion.