THE NONLINEAR EVOLUTION OF MODULATED WAVES IN A BOUNDARY-LAYER

Thee series of experiments by Schubauer and Skramstad (1948) provided the first experimental evidence of the role that the instability of To llmien-Schlichting waves played in the transition of a zero pressure-g radient flat plate boundary layer. The initial experiments studied the oscillations in the boundary layer excited by the freestream fluctuat ions. This was only possible after the background disturbances in the wind tunnel had been reduced to a very low level. The background wind tunnel environment excited a broad band of amplitude modulated disturb ance waves that grew as they propagated downstream, eventually leading to the formation of turbulent spots. Further experiments used artific ial two-dimensional harmonic excitation to produce regular wavetrains that could be directly compared with linear theory. Unfortunately, two -dimensional harmonic excitation of this type has also been used in ma ny of the subsequent nonlinear transition investigations; the modulati on of the disturbance waves, essential in nonlinear studies, has been largely ignored. Gaster and Grant (1975) used a short duration acousti c pulse to excite the boundary layer and found that the modulated wave packet that was created admitted bursts of high frequency oscillations . These occurred at amplitudes that were insufficient to generate non- linear behaviour in purely periodic wavetrains. Gaster (1980) suggeste d that the modulation of the wavepacket played an important role in th e non-linear region of transition. This investigation used computer ge nerated deterministic white noise to excite the boundary layer on a fl at plate through a single buried loudspeaker. This type of excitation produced amplitude modulated T-S waves at some point downstream from t he source. By repeatedly exciting the boundary layer with the same whi te noise sequence it was possible to map the entire flow-field with a single hot-wire probe and so study the evolution of the modulated wave trains and the eventual development of turbulent spots. The modulated wavetrains were found to grow initially according to linear theory. Bu t downstream, departures from the linear pattern were observed at isol ated time instants. The amplitude of the irregular portions of the sig nal increased rapidly with downstream distance until bursts of oscilla tions of frequencies five or six times the basic T-S frequency were ob served. These regions developed even higher frequency bursts until a t urbulent spot could be considered to have formed. Excitation signals o f various amplitudes with different phase relations between the spectr al components were used in these experiments. It was found that the ph ases between the Fourier components played an important role in the hi ghly non-linear behaviour that is the precursor to a turbulent spot. N ovel signal processing techniques, such as the wavelet transform and S ingular Value Decomposition were used to investigate the fine structur e and the propagation characteristics of the high frequency disturbanc es.