Rayleigh-Benard Instability

This lecture covers the Rayleigh-Benard instability, a phenomenon where most flows become unstable due to buoyancy forces, leading to various instabilities such as vortex shedding, flow separation, and meandering instability. The instructor discusses the physical mechanisms, equations, base state, and linearized equations involved in the analysis of this instability. The lecture also explores the dispersion relation and the factors affecting the stability of the system, such as diffusive and advective time scales. Additionally, the presentation delves into the Navier-Stokes and Oberbeck-Boussinesq equations, perturbation expansions, and the non-dimensionalization of the system.