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Explore the method of normal modes as a fundamental approach to analyzing hydrodynamic stability in this 34-minute lecture. Begin with normal modes in discrete degree-of-freedom systems before extending to continuous systems, enhanced by experimental observations. Learn to represent flow disturbances and perturbations in normal mode form for linear stability analysis, with a detailed examination of plane Poiseuille flow leading to the Orr–Sommerfeld equation derivation. Investigate the Kelvin–Helmholtz instability through Rayleigh equation analysis, then delve into boundary layer instabilities focusing on Tollmien–Schlichting (T–S) waves. Understand the characteristics of disturbances and flow conditions that trigger these instabilities, concluding with guidance for advanced study in hydrodynamic stability theory.
