Stability of non-parallel flow in a channel

Abstract

This is a review of several generalizations of Hiemenz's classic solution for steady two-dimensional flow of a uniform incompressible viscous fluid near a stagnation point on a bluff body. These generalizations are diverse exact solutions, steady and unsteady, two- and three-dimensional, of the Navier-Stokes equations. The solutions exhibit many types of instability and bifurcation. There are turning points, trans critical bifurcations, pitchfork bifurcations, Hopf bifurcations and Takens-Bogdanov bifurcations. The solutions also take the period-doubling and Ruelle-Takens routes to chaos.