Rayleigh Taylor: Normal Mode Expansion

This lecture covers the normal mode expansion in the context of Rayleigh Taylor instability, focusing on the Fourier transform in space and time, the solution to Laplace equation, and the dispersion relation analysis. It also delves into the lubrication approximation and the flattened kinematic boundary conditions. The instructor discusses the eigenvalue problem arising from the boundary conditions and the stability analysis based on the dispersion relation. The lecture concludes with a detailed exploration of the dispersion relation and the implications of different wave behaviors. Additionally, the scaling of the Stokes equations for a thin liquid film and the simplified and dimensionless forms of the governing equations are presented.