On subharmonic instability in boundary layers
The subharmonic instability in two-dimensional boundary layer on a flat plate is analyzed using the parametric instability model and the resonant triad model. The problems arising from both models are solved numerically using the shooting technique and results are presented. It is found that in the presence of a strong interaction (e.g., large amplitude of the two-dimensional wave), results from the resonant triad model are inaccurate as compared with the experimental data and the t results from the parametric instability model. This is mainly because the resonant triad model is a weakly nonlinear model, and it does not account for the modification of the eigenfunctions of the interacting waves which really takes place as we find out from the experiments.
The parametric instability model is a powerful model, despite all the assumptions included. The model, however, does not introduce a clear understanding of how the subharmonic mode originates from the three-dimensional Tollmien-Schlichting modes.
For a weak interaction results from the resonant triad model and the parametric instability model get close to each other.