Nonlinear interaction of waves in boundary-layer flows

First-order nonlinear interactions of Tollmien-Schlichting waves of different frequencies and initial amplitudes in boundary-layer flows are analyzed by using the method of multiple scales. For the case of two waves, a strong nonlinear interaction exists if one of the frequencies is twice the other frequency. Numerical results for flow past a flat plate show that this interaction mechanism is strongly destabilizing even in regions where either the fundamental or its harmonic is damped in the absence of the interaction.