Spatial Stability Analysis: Part 2

This lecture covers various types of flow instabilities, including Rayleigh-Taylor, Rayleigh Plateau, Rayleigh-Benard, Taylor Couette-Centrifugal, Kelvin-Helmholtz, and transient growth. It also discusses the transfer function of stable dynamical systems and 2D parallel flow concepts such as hyperbolic tangent mixing layers and broken-line profile mixing layers. The instructor explains how to solve the Rayleigh equation for real and complex values of k and w, as well as the polynomial eigenvalue problem. The lecture concludes with spatio-temporal spectral analysis and the concept of group velocity in the context of spatial wave stability.