HOPF BIFURCATIONS IN PLAN POLSEUILLE FLOW

We calculated the development of the 2D finiteamplitude waves in planePoiseuille flow by means of direct numerical simulation. We obtained the 2D nonlinear stable equilibrias and Hopf bifurcations occur when the equilibriaJs loss the stability in Re 3950. While second bifurcations occur,eddy near the walls moves into the core and act as the core flow. As the Revnolds number Re increases further,the flow changes into all random.