Lecture
This lecture covers the transition from Euler equations to streamfunction equation, discussing kinematic boundary conditions, perturbed kinematic boundary conditions, normal mode expansion, and the dispersion relation. It also explores the influence of stratification, surface tension, and their joint effect on flow stability, as well as Kelvin-Helmholtz instability and toroidal vortices. The presentation emphasizes the mathematical derivations and physical interpretations of the concepts presented.