Gravity Waves and Instabilities

This lecture covers perturbation theory, perturbations in compressible fluids, sound waves, instabilities in stratified fluids, highly compressible and nearly incompressible limits, energy equations, density distributions, and pressure calculations. The instructor discusses the dispersion relation, convection zones, coronas, radiative zones, and the interior of the Sun. The lecture also explores potential flows, continuous pressure conditions, and the evolution of various fluid systems, including surface gravity waves and Kelvin-Helmholtz instabilities.