PSE方法研究平板边界层中三波共振的非线性作用机制

The PSE approach to study the nonlinear evolution of three-dimensional disturbances in incompressible boundary layers on flat-plate

用抛物化稳定性方程(PSE)方法数值模拟了实验中三波共振中三维扰动的非线性作用情况,得到的计算结果与实验数据在定量上比较相符。研究表明扰动演化的定性行为与理论描述的结果是一致的,即二维波在初始阶段和参数共振阶段按照线性指数增长,三维波在初始阶段同样按照线性指数增长。在非线性作用比较强时,三维波快速增长起来,最终作用在二维波上,使其再次增长起来,从而引起转捩。

The study of the nonlinear evolution of three-dimensional disturbances in the boundary layers has a great theoretical research significance to the hydrodynamic stability. PSE method is adopted to study the subharmonic resonance in the experiment, and comparison be- tween PSE results and experimental data is presented. The numerical results by PSE match the experiment results basically in quantitatively. In the qualitative comparison, the plane wave ex- periences a linear exponential growth in the beginning stage and parametric-resonance stage, and the subharmonic oblique waves also experience a linear exponential growth in the initial stage. However, when the nonlinear effects is relatively strong, the subharmonic oblique waves experi- ence a super exponential growth that is faster than the exponential growth predicted by the linear theory, and stmulate the plane wave to make it increase again. This result is a consistent with the theoretical descriotion.