Receptivity of boundary layers to three-dimensional disturbances

The 3D receptivity of 2D laminar boundary layers to localized surface vibrations has been investigated both experimentally and theoretically for two types of basic flow: (i) the Blasius boundary layer and (ii) a boundary layer with a negative streamwise pressure gradient (Hartree parameter β_H=0.10). For the boundary-layer excitation, a specially designed surface vibrator was used. The development of the excited wave-trains was measured by means of hot-wire anemometry and decomposed into oblique normal Tollmien–Schlichting-modes. The initial spectra of the excited perturbations at the position of the vibrator was obtained by two different techniques. The first used an additional source which was mounted upstream and provided the amplification curves for the instability modes in the vicinity of the vibrator, the second was based on linear stability calculations. The receptivity coefficients were defined as the ratio of the initial wavenumber spectrum of the excited TS-waves and the corresponding resonant spectrum of the surface vibrations. They were determined for each fixed frequency as a function of the spanwise wavenumber.The boundary value problem for the disturbance produced by the vibrating membrane was solved theoretically for the same conditions as in the experiments in the framework of the classical hydrodynamic stability theory. The Navier–Stokes equations were linearized around a incompressible basic flow described by a solution of the Falkner–Skan equation. Comparisons of the theoretical and experimental results on the 3D receptivity show good quantitative agreement. It is concluded that the favorable pressure gradient increases the boundary-layer receptivity to surface vibrations.