Instability: optimal perturbations and lift-up mechanisms

This lecture covers the instability of various flow types, including pipe flow, plane Poiseuille flow, and plane Couette flow. It discusses the spectrum of different flow types, edge states, transient growth, eigenvalues, bi-orthogonal basis, non-monotonous energy evolution, and the definition of optimal gain of a linear system. The lecture also explores the Orr mechanism, lift-up mechanisms, and the projection by scalar product with adjoint vectors. It delves into the lift-up mechanism in boundary layers, streamwise vortices, and the transformation of vortices into streaks. Additionally, it examines the lift-up mechanism in a square duct, bye-pass transition to turbulence, and fully developed turbulence.