A short look at nonlinear hydrodynamic stability theory

Using a technique of Lyapounov-Schmidt type, derived from bifurcation theory, and perturbation methods coupled with multiple scales, we present a unified theory of nonlinear hydrodynamic stability. We stress the difference between the case of purely discrete normal modes and the one of continuously spread modes, according to linear theory. For the latter case we again stress the difference between Tollmien-Schlichting and convection waves, the latter being ruled by quadratic interaction of modes.