Nonlinear instabilities of a non-self-similar boundary layer on an airfoil: Experiments, DNS, and theory

The joint study provides a complete set of data, starting from the base flow and stability characteristics up to non-linear disturbance development with different involved wave triplets. The phase synchronization mechanism is investigated in detail as well as the resonance efficiency for tuned cases with respect to the exact subharmonic frequency. In general, a good agreement between the experiment, DNS and WNT is found. The essential non-self-similarity of the airfoil boundary layer does not prevent strong resonant interactions and in accordance with investigations in self-similar flows, rapid, close to double-exponential amplification of subharmonic modes is observed. At the resonant stage, the phase-synchronization condition is shown to be satisfied, which provides equal phase speeds for all involved modes. For tuned cases, the initial phase relation between fundamental and subharmonic modes can lead, partly, to a suppression of the subharmonic wave amplification. Variation of the fundamental wave frequency shows that the integral resonance efficiency is significantly decreased with the reduction of the frequency. This effect is explained as a frequency dependence of the nonlinear coupling coefficients as well as the detuning of the subharmonic-fundamental phase speed associated mainly with the base-flow non-self-similarity. Depending on the frequency content of the initial disturbances this can lead to a direct influence on the corresponding transition position.