Secondary instability in boundary-layer flows

The stability of a secondary Tollmien-Schlichting wave, whose wavenumber and frequency are nearly one half of those of a fundamental Tollmien-Schlichting instability wave (T-S wave), is analyzed by using the method of multiples. Under these conditions, the fundamental wave acts as a parametric excitor for the secondary wave. When the amplitude of the fundamental wave is small, the amplitude of the secondary wave deviates slowly from its unexcited state. However, as the amplitude of the fundamental wave increases, so does the amplitude of the secondary wave even in the regions where it is damped in the unexcited state.