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

  • 摘要: 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。

     

    Abstract: 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 between 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 experiences 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 experience 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 description.

     

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