The three-dimensional resonant interaction of a plane Tollmien-Schlichting wave, having a frequency f1, with a pair of oblique waves having frequencies ½ f1, 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 f1, 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 f1 + Δf for different values of the frequency detuning Δf. 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.
The present experimental study is devoted to examination of the vortex receptivity mechanism associated with excitation of unsteady cross-flow (CF) waves due to scattering of unsteady free-stream vortices on localized steady surface non-uniformities (roughness). The measurements are carried out in a low-turbulence wind tunnel by means of a hot-wire anemometer in a boundary layer developing over a 25 • swept-wing model. The harmonic-in-time free-stream vortices were excited by a thin vibrating wire located upstream of the experimental-model leading edge and represented a kind of small-amplitude von Kármán vortex street with spanwise orientation of the generated instantaneous vorticity vectors. The controlled roughness elements (the so-called 'phased roughness') were placed on the model surface. This roughness had a special shape, which provided excitation of CF-waves having basically some predetermined (required) spanwise wavenumbers. The linearity of the stability and receptivity mechanisms under study was checked accurately by means of variation of both the free-stream-vortex amplitude and the surface roughness height. These experiments were directed to obtaining the amplitudes and phases of the vortexroughness receptivity coefficients for a number of vortex disturbance frequencies. The vortex street position with respect to the model surface (the vortex offset parameter) was also varied. The receptivity characteristics obtained experimentally in Fourier space are independent of the particular roughness shape, and can be used for validation of receptivity theories.
This work brings together experimental and theoretical studies of nonlinear stages aimed at the K-regime in boundary-layer transition, and some combined theoretical and experimental results are discussed. It is shown that the initial stages in the formation of so-called spikes, observed in many experiments, may be described very well by the asymptotic theory. These flashes-spikes are shown to be (in certain regimes) possible solitons of the boundary layer and governed by the integral-differential Benjamin-Ono equation. Properties of the spike-solitons, obtained both theoretically and experimentally in the quasi-planar stages of their development, are presented. Features of the disturbance behaviour connected with the subsequent development of three-dimensionality are also discussed, as are the effects of viscosity and shorter lengthscales. The main conclusion of the work concerns the hypothesis of the possible soliton nature of the flashes-spikes (within limits), which seems reliably corroborated by the good agreement found between the theory and the experimental data.
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