Numerical simulations of multifrequency instability-wave growth and suppression in the Blasius boundary layer

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Abstract
A mathematical model based on the Orr–Sommerfeld equation is developed to describe the growth and suppression of multifrequency, two-dimensional instability waves in the Blasius boundary layer over a flat place through localized perturbations at the surface caused by time-varying suction/blowing. It is shown for harmonic (single-frequency) perturbations that the instability wave can be decomposed into two components: an idealized Tollmien–Schlichting wave and a second perturbation that approximately cancels the first component upstream of the surface disturbance and becomes small downstream. Because the first component alone fully expresses the instability of the flow, the need to perform numerical Fourier transformation over the wave number is eliminated, permitting easy extension of the analysis to the more general case of arbitrary waveform of the perturbation. Numerical results are presented for examples of instability-wave generation and suppression in the boundary layer.