Abstract

First-order nonlinear interactions of streamwise vortices with different amplification rates, spanwise wave numbers, and initial amplitudes in boundary layer flows on concave walls are studied by using the method of multiple scales. Numerical results show that the effect of interaction between two vortices in harmonic resonance is strong when the amplitude of the secondary wave (higher harmonic) has reached certain % of the mean flow. In combination resonance between three waves, it is found that the two primary waves with moderate initial amplitudes have a strong influence on their difference harmonic wave. The resonant interaction between waves of higher wave numbers causes strong amplification at earlier stages (at lower values of G) than the resonant interaction between waves of lower wave numbers.

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