Asymptotic Center-Manifold for the Navier-Stokes

Abstract: The dynamics of bifurcating fluid systems are typically studied using weakly-nonlinear analysis. In this blackboard talk I show how the same problem can be approached utilizing the center-manifold theorem, resulting in a finite-dimensional system coupled to an infinite-dimensional graph equation. Asymptotic approximations of the graph equations are shown to have a simple and universal structure.The theory is then applied to the case of Hopf bifurcation in the cylinder wake and the flow in an open cavity.