The resonant interaction of disturbances at laminar-turbulent transition in a boundary layer

TLDR

Laminar‑flow breakdown can occur via various mechanisms, which are discussed in the study. The study examined resonant wave interactions in a boundary layer by adding a priming oscillation at \(f'=\tfrac12 f_1+\Delta f\) across a range of detuning values. The experiment revealed a three‑dimensional resonant interaction between a Tollmien‑Schlichting wave and oblique waves at half its frequency, producing parametric resonance that amplifies background oscillations and underscoring the interaction’s importance for boundary‑layer transition.

Abstract

The three-dimensional resonant interaction of a plane Tollmien-Schlichting wave, having a frequency f 1 , with a pair of oblique waves having frequencies ½ f 1 , was observed and studied experimentally. In the initial stages, the interaction proved to be a parametric resonance, resulting in the amplification of small random priming (background) oscillations of frequency ½ f 1 , and of a packet of low-frequency oscillations. The resonant interaction of waves in a boundary layer was investigated also by introducing a priming oscillation with frequency f ’ = ½ f 1 + Δ f for different values of the frequency detuning Δ f . The importance of the discovered wave interaction in boundary-layer transition is demonstrated. Causes of realization of different types of laminar-flow breakdown are discussed.