Receptivity of boundary layers to distributed wall vibrations

Linear three-dimensional receptivity of boundary layers to distributed wall vibrations in the large Reynolds number limit (Re??) is studied in this paper. The fluid motion is analysed by means of the multiscale asymptotic technique combined with the method of matched asymptotic expansions. The body surface is assumed to be perturbed by small-amplitude oscillations being tuned in resonance with the neutral Tollmien–Schlichting wave at a certain point on the wall. The characteristic length of the resonance region is found to be O(Re-3/16), which follows from the condition that the boundary-layer non-parallelism and the wave amplitude growth have the same order of magnitude. The amplitude equation is derived as a solvability condition for the inhomogeneous boundary-value problem. Investigating detuning effects, we consider perturbations in the form of a wave packet with a narrow O(Re-3/16) discrete or continuous spectrum concentrated near the resonant wavenumber and frequency. The boundary-layer laminarization based on neutralizing the oncoming Tollmien–Schlichting waves (or wave packets) is also discussed