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

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.