Thermal Instabilities: Rayleigh-Benard Analysis

This lecture covers various fluid instabilities, including Rayleigh-Taylor, Tollmien-Schlichting, and Rayleigh-Benard. The focus is on the Rayleigh-Benard instability, analyzing its physical mechanism, equations, base state, linearized equations, normal mode expansion, and dispersion relation. The lecture also discusses the critical length, diffusive and advective time scales, and the threshold for instability. Key concepts such as buoyancy force, drag force, and the effects of temperature gradients on stability are explored.