Lecture
This lecture covers the analysis of instability in fluid dynamics, focusing on linearized equations and dispersion relation. Starting with the base state and dynamic boundary conditions, it progresses to the perturbation and linearization of the Euler equations. The lecture then delves into the normal mode expansion and the Laplace equation for pressure. Key topics include the dynamic boundary conditions, radial velocity retrieval, and the impact of surface tension on stability. The discussion culminates in the examination of the dispersion relation, determining the stability of the flow based on the wavenumber and frequency.