用弱非线性理论研究二次稳定性问题

本文把研究三波共振的弱非线性理论应用于平板边界层和平面Poiseuille流三维扰动的二次稳定性问题。其数值结果与文献1]、2]用Floquet形式的二次稳定性理论得出的结论是一致的。

Investigation of The Problem of Secondary Instability by Weakly Nonlinear Theory

In the paper the artificial neutral method proposed in 6] is used to seek for a two dimentional equilibrium solutions with finite amplitude, and then the expansion method of the weakly nonlinear theory is applied to solve the secondary instability equations of plate boundary layer and plane poiseuille flow. The numerical results show that the three dimensional disturbances have strong growth rates and the resonant conditions can be satisfied in a band of the frequency. For boundary layer threshold phenomenon has not been found in the range between two branches of the neutral curves, but it has beyond this range. The value of the threshold amplitude of plane poiseuille flow is consistent with those reported in Ref.1].