Hydrodynamic Instabilities: Part 2

This lecture covers the physical mechanisms behind Kelvin-Helmholtz instability, including the dispersion relation and kinematic boundary conditions. It delves into 2D parallel flow concepts, linearized equations, and perturbed kinematic boundary conditions. The lecture also explores normal mode expansion, the solution to Laplace equation, and perturbed and linearized Euler equations. Furthermore, it discusses the dispersion relation, the influence of stratification and surface tension, and the joint influence of both. The lecture concludes with applications of Kelvin-Helmholtz instability in geophysics and the formation of toroidal vortices and vortex rings.