Receptivity and Growth of Two- and Three-Dimensional Disturbances in a Blasius Boundary Layer

In this experimental study, acoustic receptivity was examined for a Blasius boundary layer formed on a flat plate. Non-localized surface roughness, 2-D and oblique, were considered for various roughness heights and acoustic wave amplitudes. The receptivity sites (surface roughness) had a well defined wavenumber spectrum with a fundamental wavenumber of kw. A planar downstream-traveling acoustic wave was created to temporally excite the flow near the resonance frequency, ωts, of an unstable eigenmode corresponding to kts = kw. Branch I was selected to occur near the streamwise center of the roughness to maximize the receptivity. The range of acoustic forcing levels and roughness heights ∆h examined resulted in a linear dependence of receptivity coefficients; however, the larger values of the combination · ∆h resulted in subsequent nonlinear development of the Tollmien-Schlichting (T-S) wave. The measured receptivity was seen to increase markedly with increasing obliqueness of the surface roughness patterns. Detuning of the 2-D and oblique disturbances was investigated by varying the streamwise wall-roughness wavenumber αw and measuring the T-S response. Oblique transition was also investigated by exciting a pair of oppositely-oriented oblique Orr-Sommerfeld modes (ω/ωts,±β/βw) = (1,±1). For small values of ·∆h, a peak-valley structure corresponding to a spanwise wavenumber of 2βw was observed. The maximum streamwise velocity fluctuations, ut(fo), occur at peak locations as expected. For the largest value of ·∆h, significant mean-flow distortion was observed in the mean streamwise velocity. Large spanwise velocity gradients, |dU/dζ|, exist between peaks and valleys and appear to generate a secondary instability. The maximum values of ut no longer occur at peak locations of the stationary structure but at locations of spanwise inflection points. The magnitude of ut scales with |dU/dζ|. A nonlinear interaction of two nonstationary modes was conjectured as a possible mechanism for the enhancement of the streak amplification rate. This is the Ph.D. thesis of Rudolph King, submitted to the Department of Aeronautics and Astronautics at the Massachusetts Institute of Technology in November 1999, supervised by Professor Kenneth S. Breuer. All inquiries should be directed to either Rudy King at [email protected] or Kenneth Breuer at [email protected].