Inviscid Instabilities: Rayleigh Criterion

This lecture covers the concepts of parallel flow instabilities, including the effects of surface tension and gravity, the Rayleigh inflection point criterion, and the normal mode decomposition in the context of 3D Euler equations. It delves into the linear Euler equations, 3D dispersion relations, Squire's transformation, and the Rayleigh theorem of 1916. The lecture also explores the implications of Rayleigh's inflection point criterion for the stability of basic flows and provides insights into solving the Rayleigh equation using finite differences of order 1.