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The paper is devoted to experimental investigation of an efficient mechanism of distributed excitation of nonstationary Gortler vortices in a boundary layer on concave wall due to scattering of three-dimensional, streamwise oriented freestream vortices on natural two-dimensional base-flow nonuniformity associated with the boundary layer growth. The investigations are performed in a broad range of disturbance frequencies and spanwise wavenumbers. The measurements have shown that the distributed receptivity mechanism is able to modify significantly the disturbance growth rates. This mechanism is found to be able to compete successfully with the linear instability mechanism. It is found that at relatively low frequencies and not too large freestream disturbance amplitudes, the Gortler modes’ development is dominated basically by the corresponding linear instability mechanism. Meanwhile, this mechanism becomes weaker with growth of frequency and, simultaneously, the distributed receptivity mechanism gets stronger. This leads to enhancement of role of the latter in amplification of Gortler instability modes, and at high frequencies the role of the distributed receptivity mechanism becomes very important and often even decisive one. Based on deep processing of the experimental data, quantitative values of the distributed linear receptivity coefficients are obtained for the case of excitation of unsteady Gortler modes and estimated for the case of steady Gortler vortices by means of extrapolation to the zero frequency. A complementary experiment devoted to investigation of the problem of linear unsteady Gortler instability is performed for the particular conditions of the distributed receptivity experiments. All main stability characteristics are obtained and compared with calculated ones. In general, the experimental information presented in this paper can be used for verification of various instability and vortex receptivitytheories.

The subject of the present combined experimental and theoretical investigation is the steady and unsteady linear Gortler instability. The majority of previous experiments were devoted to the steady Gortler vortices, despite the unsteady ones are also observed in real transitional flows. Moreover, even for the steady Gortler vortices no quantitative agreement between the experimental and theoretical linear-stability characteristics was obtained, especially for disturbance amplification rates. The experimental difficulties were connected, in particular, with a rather poor accuracy of measurements at zero disturbance frequency, a possible influence of nonlinearity, and an admixture of non-modal (transient) growth mechanism. All these difficulties have been overcome in the experimental part of the present study by means of: (i) tuning-out of the exact zero frequency of Gortler vortices and working, instead, with quasi-steady perturbations of very low frequencies, (ii) performing measurements at low disturbance amplitudes, and (iii) minimization and careful estimation of the disturbance-source near-field by means of utilizing a special controlled disturbance source and performing special numerical computations for exact experimental conditions. A detailed study of all linear-stability characteristics for essentially unsteady Gortler vortices was performed in this paper as well. The results are obtained in a range of Gortler numbers 13 ≲ Go ≲ 17.3, frequency parameters F = 0.56–22.70, and spanwise wavelength parameters Λ = 149–775 (close to the most amplified Gortler modes). Appropriate calculations based on locally-parallel and non-local non-parallel linear-stability theories were performed and compared quantitatively with experimentally obtained linear-stability characteristics. For the first time all stability characteristics measured for steady Gortler vortices (in quasi-steady regimes) are found to agree very well with those calculated for the most amplified first discrete-spectrum mode of the linear Gortler-instability problem. Similar good agreement is obtained for essentially unsteady Gortler vortices. The roles of effects of the base-flow non-parallelism and the disturbance-source near-field are examined.

The three-dimensional acoustic receptivity of laminar boundary layers in presence of microscopic surface vibrations (the vibro-acoustic receptivity) is examined. The flow under investigation is the boundary layer on an airfoil at relatively high Reynolds numbers close to realistic ones for gliders. This flow has favourable and adverse pressure gradients and develops on a curved wall. The goal of the present study is to obtain quantitative information about the receptivity characteristics of this flow for excitation of the 3D Tollmien–Schlichting (TS) waves in cases when the frequencies of surface vibrations ( f v ) have the same order of magnitudes as those of the acoustic waves ( f ac ) . The experiments were performed at controlled disturbance conditions. The 2D acoustic field was produced by loudspeakers, while the localised non-stationary surface non-uniformities were simulated by a controlled circular surface vibrator. The TS-wave generation was investigated for several values of the parameter of non-stationarity of the surface non-uniformity K = f v / f ac . The receptivity was investigated in two general cases: in ‘plus-regimes’ when the TS-waves were excited at combination frequencies f TS + = f ac + f v and in ‘minus-regimes’ when the excitation occurred at frequencies f TS − = f ac − f v . The complex (amplitude and phase) receptivity coefficients are obtained experimentally as functions of the spanwise wavenumber (and the wave propagation angle) for three different frequency ratios K and also for several TS-wave frequencies at fixed values of K. The obtained vibro-acoustic receptivity coefficients are compared with the acoustic-roughness receptivity coefficients (i.e. for K = 0 ) found in previous experiments and DNS.

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 βH=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.