平面Poisenille流动的二维Hopf分叉

HOPF BIFURCATIONS IN PLAN POLSEUILLE FLOW

本文用直接数值模拟的方法计算了二维Ｐｏｉｓｅｕｉｌｌｅ流动中扰动波的演化问题。得到了二维平衡态，在一定的波数下，Ｒｅ３９５０时，这种平衡态，将变得不稳定，模拟发现出现第二周期解，即二次分叉。

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.