Linear Stability Analysis in Fluid Dynamics

This course covers the comprehensive understanding of stability theory and analysis in fluid dynamics. It begins with the exploration of the transition from laminar to turbulent flows, emphasizing the critical significance of the Reynolds number's. The course introduces the concept of perturbations in parallel flows and their analysis using linear stability analysis. It further explains the Fourier analysis and Squire's theorem application to simplify the momentum equation into the Orr-Sommerfeld equation. The course also delves into the non-dimensional form of the equation, viscous stability, stability maps, and the boundary conditions required to solve the equation. It concludes with the stability analysis of inviscid flow, focusing on the Rayleigh's equation and Orr Sommerfeld equation, and their application to different types of flows. The course also discusses the necessary conditions for inviscid instability, including the Rayleigh's inflection point theorem and Fjortoft's theorem.